Binomial expansion of (1+ (3-2*sqrt(2)))^n
(1+x)^n = sum_{k=0..n} ((n!/((n-k)!*k!))*x^k; x = 3-2*sqrt(2)
n
0
1
1
2
2
2
3
3
3
3
4
4
4
4
4
5
5
5
5
5
5
6
6
6
6
6
6
6
7
7
7
7
7
7
k
0
0
1
0
1
2
0
1
2
3
0
1
2
3
4
0
1
2
3
4
5
0
1
2
3
4
5
6
0
1
2
3
4
5
n!/(n-k)!*k!
1
1
1
1
2
1
1
3
3
1
1
4
6
4
1
1
5
10
10
5
1
1
6
15
20
15
6
1
1
7
21
35
35
21
x^k
(n!/(n-k)!*k!)*x^k
1
1
(3-2sr2)^0
1
(3-2sr2)^1
(3-2sr2)^1
(3-2sr2)^0
1
(3-2sr2)^1
2*(3-2sr2)^1
(3-2sr2)^2
(3-2sr2)^2
(3-2sr2)^0
1
(3-2sr2)^1
3*(3-2sr2)^1
(3-2sr2)^2
3*(3-2sr2)^2
(3-2sr2)^3
(3-2sr2)^3
(3-2sr2)^0
1
(3-2sr2)^1
4*(3-2sr2)^1
(3-2sr2)^2
6*(3-2sr2)^2
(3-2sr2)^3
4*(3-2sr2)^3
(3-2sr2)^4
(3-2sr2)^4
(3-2sr2)^0
1
(3-2sr2)^1
5*(3-2sr2)^1
(3-2sr2)^2
10*(3-2sr2)^2
(3-2sr2)^3
10*(3-2sr2)^3
(3-2sr2)^4
5*(3-2sr2)^4
(3-2sr2)^5
(3-2sr2)^5
(3-2sr2)^0
1
(3-2sr2)^1
6*(3-2sr2)^1
(3-2sr2)^2
15*(3-2sr2)^2
(3-2sr2)^3
20*(3-2sr2)^3
(3-2sr2)^4
15*(3-2sr2)^4
(3-2sr2)^5
6*(3-2sr2)^5
(3-2sr2)^6
(3-2sr2)^6
sum
1
1
3-2sr2
1
2*(3 -2sr2)
17-12sr2
1
3*(3-2sr2)
3*(17-12sr2)
99-70sr2
1
4*(3-2sr2)
6*(17-12sr2)
4*(99-70sr2)
577-408sr2
1
5*(3-2sr2)
10*(17-12sr2)
10*(99-70sr2)
5*(577-408sr2)
3363-2378sr2
1
6*(3-2sr2)
15*(17-12sr2)
20*(99-70sr2)
15*(577-408sr2)
6*(3363-2378sr2)
19601-13860sr2
1
7*(3-2sr2)
21*(17-12sr2)
35*(99-70sr2)
35*(577-408sr2)
21*(3363-2378sr2)
A084130
a(n) + b(n)*sqrt(2)
a(n)
b(n)
1
0
4
-2
3
2
24
-16
6
4
17
12
160
-112
9
6
51
36
99
70
1088
-768
12
8
102
72
396
280
577
408
7424
-5248
15
10
170
120
990
700
2885
2040
3363
2378
50688
35840
18
12
255
180
1980
1400
8655
6120
20178
14268
19601
13860
346112
244736
21
14
357
252
3465
2450
20195
14280
70623
49938
A248599
b(n)/2
0
-1
-8
-56
-384
-2624
-17920
-122368
7
7
8
8
8
8
8
8
8
8
8
9
9
9
9
9
9
9
9
9
9
10
10
10
10
10
10
10
10
10
10
10
11
11
11
11
11
11
11
6
7
0
1
2
3
4
5
6
7
8
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
1
1
8
28
56
70
56
28
8
1
1
9
36
84
126
126
84
36
9
1
1
10
45
120
210
252
210
120
45
10
1
1
11
55
165
330
462
462
7*(19601-13860sr2)
114243-80782sr2
1
8*(3-2sr2)
28*(17-12sr2)
56*(99-70sr2)
70*(577-408sr2)
56*(3363-2378sr2)
28*(19601-13860sr2)
8*(114243-80782sr2)
665857-470832sr2
1
9*(3-2sr2)
36*(17-12sr2)
84*(99-70sr2)
126*(577-408sr2)
126*(3363-2378sr2)
84*(19601-13860sr2)
36*(114243-80782sr2)
9*(665857-470832sr2)
3880899-2744210sr2
1
10*(3-2sr2)
45*(17-12sr2)
120*(99-70sr2)
210*(577-408sr2)
252*(3363-2378sr2)
210*(19601-13860sr2)
120*(114243-80782sr2)
45*(665857-470832sr2)
10*(3880899-2744210sr2)
22619537-15994428sr2
1
11*(3-2sr2)
55*(17-12sr2)
165*(99-70sr2)
330*(577-408sr2)
462*(3363-2378sr2)
462*(19601-13860sr2)
137207
114243
2363392
24
476
5544
40390
188328
548828
913944
665857
16138240
27
612
8316
72702
423738
1646484
4112748
5992713
3880899
110198784
30
765
11880
121170
847476
4116210
13709160
29963565
38808990
22619537
752484352
33
935
16335
190410
1553706
9055662
97020
80782
1671168
16
336
3920
28560
133168
388080
646256
470832
11411456
18
432
5880
51408
299628
1164240
2908152
4237488
2744210
77922304
20
540
8400
85680
599256
2910600
9693840
21187440
27442100
15994428
532086762
22
660
11550
134640
1098636
6403320
-835584
-5705728
-38961152
-266043381
11
11
11
11
11
12
12
12
12
12
12
12
12
12
12
12
12
12
13
13
13
13
13
13
13
13
13
13
13
13
13
13
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
12
0
1
2
3
4
5
6
7
8
9
10
11
12
13
330
165
55
11
1
1
12
66
220
495
792
924
792
495
220
66
12
1
1
13
78
286
715
1287
1716
1716
1287
715
286
78
13
1
330*(114243-80782sr2)
165*(665857-470832sr2)
55*(3880899-2744210sr2)
11*(22619537-15994428sr2)
1318836323-93222358sr2
1
12*(3-2sr2)
66*(17-12sr2)
220*(99-70sr2)
495*(577-408sr2)
792*(3363-2378sr2)
924*(19601-13860sr2)
792*(114243-80782sr2)
495*(665857-470832sr2)
220*(3880899-2744210sr2)
66*(22619537-15994428sr2)
12*(1318836323-93222358sr2)
768398401-543339720sr2
1
13*(3-2sr2)
78*(17-12sr2)
286*(99-70sr2)
715*(577-408sr2)
1287*(3363-2378sr2)
1716*(19601-13860sr2)
1716*(114243-80782sr2)
1287*(665857-470832sr2)
715*(3880899-2744210sr2)
286*(22619537-15994428sr2)
78*(1318836323-93222358sr2)
13*(768398401-543339720sr2)
4478554083-3166815962sr2
37700190
109866405
213449445
248814907
131836323
5138284544
36
1122
21780
285615
2663496
18111324
90480456
329599215
853797780
1492889442
1582035876
768398401
35086401536
39
1326
28314
412555
4328181
33635316
196040988
856957959
2774842785
6469187582
10283233194
9989179213
4478554083
26658060
77687280
150931550
175938708
93222358
3633315840 -1816657920
24
792
15400
201960
1883376
12806640
63979344
233061840
603726200
1055632248
1118668296
543339720
24809832448 -12404916224
26
936
20020
291720
3060486
23783760
138621912
605960784
1962110150
4574406408
7271343924
7063416360
3166815962