A004171 -id:A004171 - cp's OEIS frontend

A220579 T(n,k)=Equals one maps: number of nXk binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 nXk array.

1, 2, 1, 4, 8, 1, 8, 21, 32, 1, 16, 115, 91, 128, 1, 32, 371, 1441, 375, 512, 1, 64, 1504, 8334, 17505, 1487, 2048, 1, 128, 5240, 64497, 165130, 205323, 5835, 8192, 1, 256, 19904, 436288, 2652007, 3162375, 2352642, 22775, 32768, 1, 512, 71787, 3036588

Offset: 1

R. H. Hardin Dec 16 2012

Table starts
.1.......2.......4..........8..........16...........32...........64.........128
.1.......8......21........115.........371.........1504.........5240.......19904
.1......32......91.......1441........8334........64497.......436288.....3036588
.1.....128.....375......17505......165130......2652007.....33180533...450926562
.1.....512....1487.....205323.....3162375....106841503...2449921734.65126683335
.1....2048....5835....2352642....59690533...4239598056.178051989526
.1....8192...22775...26616961..1120269376.166807007000
.1...32768...88683..299065708.20961430054
.1..131072..344975.3347252663
.1..524288.1341395
.1.2097152
.1

			Some solutions for n=3 k=4
..1..1..0..0....0..1..1..1....0..0..0..1....0..0..1..1....1..0..0..1
..0..1..1..1....1..0..0..1....0..0..0..1....1..0..1..0....0..0..0..1
..1..1..0..1....1..0..0..1....1..0..1..1....0..1..0..0....1..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..82

Column 2 is A004171(n-1)

Row 1 is A000079(n-1)

A301841 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 25, 32, 8, 16, 81, 139, 128, 16, 32, 263, 678, 773, 512, 32, 64, 855, 3182, 5748, 4299, 2048, 64, 128, 2778, 15199, 39703, 48802, 23909, 8192, 128, 256, 9027, 72514, 281758, 496085, 414385, 132971, 32768, 256, 512, 29333, 346244

Offset: 1

R. H. Hardin, Mar 27 2018

Table starts
...1......2.......4.........8..........16...........32.............64
...2......8......25........81.........263..........855...........2778
...4.....32.....139.......678........3182........15199..........72514
...8....128.....773......5748.......39703.......281758........1986213
..16....512....4299.....48802......496085......5240684.......54948498
..32...2048...23909....414385.....6196305.....97439921.....1518341751
..64...8192..132971...3518619....77396422...1812097252....41966406867
.128..32768..739525..29877293...966770632..33701001773..1159968653556
.256.131072.4112907.253694309.12076215811.626769301255.32062561937804

			Some solutions for n=5 k=4
..0..1..1..0. .0..1..0..1. .0..1..1..1. .0..0..0..0. .0..0..1..1
..1..0..1..0. .1..1..0..1. .1..0..1..0. .1..1..0..1. .0..1..0..1
..1..0..1..1. .1..0..1..0. .1..0..1..1. .0..1..0..1. .1..1..0..1
..0..1..0..0. .0..0..1..0. .1..0..1..1. .0..0..1..0. .0..1..0..0
..1..0..1..0. .0..1..0..1. .1..0..0..0. .1..1..0..1. .1..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..417

Column 1 is A000079(n-1).
Column 2 is A004171(n-1).
Row 1 is A000079(n-1).

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 7*a(n-1) -8*a(n-2) for n>3
k=4: a(n) = 13*a(n-1) -46*a(n-2) +72*a(n-3) -57*a(n-4) +16*a(n-5) for n>6
k=5: [order 11] for n>13
k=6: [order 25] for n>27
k=7: [order 53] for n>56
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4) for n>6
n=3: [order 12] for n>14
n=4: [order 35] for n>38
n=5: [order 99] for n>104

A302265 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 29, 32, 8, 16, 105, 153, 128, 16, 32, 384, 772, 818, 512, 32, 64, 1405, 3818, 5922, 4386, 2048, 64, 128, 5135, 19191, 40296, 45717, 23516, 8192, 128, 256, 18766, 96004, 284428, 429854, 353229, 126162, 32768, 256, 512, 68589, 481261

Offset: 1

R. H. Hardin, Apr 04 2018

Table starts
...1......2.......4.........8.........16...........32............64
...2......8......29.......105........384.........1405..........5135
...4.....32.....153.......772.......3818........19191.........96004
...8....128.....818......5922......40296.......284428.......1984001
..16....512....4386.....45717.....429854......4289139......41994750
..32...2048...23516....353229....4608075.....64975832.....893462062
..64...8192..126162...2727755...49315068....982041385...18964765818
.128..32768..676988..21069318..527911860..14850510984..402597400706
.256.131072.3632880.162753849.5651844495.224584502616.8547940665506

			Some solutions for n=5 k=4
..0..0..1..1. .0..1..0..1. .0..1..0..1. .0..0..0..0. .0..1..1..0
..0..1..1..0. .0..1..1..0. .0..1..0..0. .0..1..1..0. .1..0..1..1
..1..1..0..0. .0..0..1..0. .0..1..0..0. .0..1..0..1. .1..1..0..0
..0..1..1..1. .1..1..0..1. .0..1..0..0. .0..1..0..1. .0..1..0..1
..1..0..0..0. .0..0..0..1. .0..1..1..1. .0..0..1..0. .1..1..0..0

R. H. Hardin, Table of n, a(n) for n = 1..180

Column 1 is A000079(n-1).
Column 2 is A004171(n-1).
Row 1 is A000079(n-1).

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 6*a(n-1) -2*a(n-2) +2*a(n-3) -54*a(n-4) +16*a(n-5) for n>6
k=4: [order 17] for n>18
k=5: [order 70] for n>71
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4)
n=3: [order 12] for n>13
n=4: [order 44] for n>45

A013776 a(n) = 2^(4*n+1).

Original entry on oeis.org

2, 32, 512, 8192, 131072, 2097152, 33554432, 536870912, 8589934592, 137438953472, 2199023255552, 35184372088832, 562949953421312, 9007199254740992, 144115188075855872, 2305843009213693952

Offset: 0

N. J. A. Sloane

a(n) ~ -Pi*E(2*n)/B(2*n), E(n) Euler number, B(n) Bernoulli number. - Peter Luschny, Oct 28 2012
Equivalently, powers of 2 with final digit 2. - Muniru A Asiru, Mar 15 2019
As phi(a(n)) = (2^n)^4 is a perfect biquadrate (where phi is the Euler totient A000010), this is a subsequence of A078164 and A307690. - Bernard Schott, Mar 28 2022

			G.f. = 2 + 32*x + 512*x^2 + 8192*x^3 + 131072*x^4 + 2097152*x^5 + ...

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Tanya Khovanova, Recursive Sequences
Index to divisibility sequences
Index entries for linear recurrences with constant coefficients, signature (16).

Subsequence of A307690.
Cf. A000010, A004171, A016813, A264960, A307690.
Intersection of A000079 and A078164.

List([0..20],n->2^(4*n+1)); # Muniru A Asiru, Mar 15 2019

[2^(4*n+1): n in [0..20]]; // Vincenzo Librandi, Jun 27 2011

[2^(4*n+1)$n=0..20]; # Muniru A Asiru, Apr 10 2019

2^(4*Range[0,20]+1) (* G. C. Greubel, Mar 15 2019 *)
NestList[16#&,2,20] (* Harvey P. Dale, Jul 28 2019 *)

a(n)=2<<(4*n) \\ Charles R Greathouse IV, Apr 07 2012

[2^(4*n+1) for n in (0..20)] # G. C. Greubel, Mar 15 2019

From Philippe Deléham, Nov 23 2008: (Start)
a(n) = 16*a(n-1), n > 0, a(0) = 2.
G.f.: 2/(1 - 16*x). (End)
From Peter Bala, Nov 29 2015: (Start)
a(n) = Sum_{k = 0..n} binomial(2*k,k)*binomial(4*n + 2 - 2*k, 2*n + 1 - k).
Bisection of A264960. (End)
a(n) = A000079(A016813(n)). - Michel Marcus, Nov 30 2015
a(n) = Sum_{k = 0..2*n} binomial(4*n + 2, 2*k + 1) = A004171(2*n). - Peter Bala, Nov 25 2016
E.g.f.: 2*exp(16*x). - G. C. Greubel, Jun 30 2019
From Bernard Schott, Apr 15 2022: (Start)
Sum_{n>=0} 1/a(n) = 8/15.
Sum_{n>=0} (-1)^n/a(n) = 8/17. (End)

Wrong comment deleted by Kevin Ryde, Apr 16 2022

A028403 Number of types of Boolean functions of n variables under a certain group.

Original entry on oeis.org

4, 12, 40, 144, 544, 2112, 8320, 33024, 131584, 525312, 2099200, 8392704, 33562624, 134234112, 536903680, 2147549184, 8590065664, 34360000512, 137439477760, 549756862464, 2199025352704, 8796097216512, 35184380477440, 140737505132544, 562949986975744

Offset: 1

N. J. A. Sloane

Harvey P. Dale, Table of n, a(n) for n = 1..1000
I. Strazdins, Universal affine classification of Boolean functions, Acta Applic. Math. 46 (1997), 147-167.
Index entries for sequences related to Boolean functions
Index entries for linear recurrences with constant coefficients, signature (6,-8).

Cf. A000051, A000079, A004171, A007582, A081294.

This sequence in base 2 is A163450. - Jaroslav Krizek, Jul 27 2009

[2^(2*n-1) +2^n: n in [1..30]]; // G. C. Greubel, Jul 07 2021

Join[{4},Table[FromDigits[Join[{1},PadRight[{},n-2,0],{1},PadRight[ {},n,0]],2],{n,2,30}]] (* Harvey P. Dale, Jan 24 2021 *)

Vec(4*x*(1-3*x)/((1-2*x)*(1-4*x)) + O(x^100)) \\ Colin Barker, Sep 30 2014

[2^(2*n-1) +2^n for n in (1..30)] # G. C. Greubel, Jul 07 2021

a(n) = (2^(n-1) + 1)*2^n = 2*A007582(n-1). - Ralf Stephan, Mar 24 2004
a(n) = A000079(n) * (A000079(n-1) + 1) = (A000051(n) - 1) * A000051(n-1) = A000079(n) * A000051(n-1) = (A000051(n) - 1) * (A000079(n-1) + 1) = 2^n * (2^(n-1) + 1). a(n+1) = A000079(n+1) * (A000079(n) + 1) = (A000051(n+1) - 1) * A000051(n) = A000079(n+1) * A000051(n) = (A000051(n+1) - 1) * (A000079(n) + 1) = 2^(n+1) * (2^n + 1). a(n) = A081294(n) + A000079(n) = A004171(n-1) + A000079(n) = 2^(2n-1) + 2^n. - Jaroslav Krizek, Jul 27 2009
From Colin Barker, Sep 30 2014: (Start)
a(n) = 6*a(n-1) - 8*a(n-2).
G.f.: 4*x*(1 - 3*x)/((1-2*x)*(1-4*x)). (End)
E.g.f.: (1/2)*(exp(2*x) -1)*(exp(2*x) + 3). - G. C. Greubel, Jul 07 2021

More terms from Vladeta Jovovic, Feb 24 2000

More terms from Colin Barker, Sep 30 2014

A208709 T(n,k)=Number of nXk 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 28, 32, 8, 16, 100, 196, 128, 16, 32, 356, 1268, 1372, 512, 32, 64, 1268, 8128, 16084, 9604, 2048, 64, 128, 4516, 52184, 185344, 204020, 67228, 8192, 128, 256, 16084, 334948, 2142580, 4226368, 2587924, 470596, 32768, 256, 512, 57284, 2149988

Offset: 1

R. H. Hardin Mar 01 2012

Table starts
...1.....2.......4.........8..........16............32..............64
...2.....8......28.......100.........356..........1268............4516
...4....32.....196......1268........8128.........52184..........334948
...8...128....1372.....16084......185344.......2142580........24754628
..16...512....9604....204020.....4226368......87985748......1830045552
..32..2048...67228...2587924....96373248....3613193828....135288700496
..64..8192..470596..32826932..2197585152..148378294612..10001404535216
.128.32768.3294172.416398420.50111214592.6093257064980.739367693888784

			Some solutions for n=4 k=3
..0..1..1....0..1..0....0..0..0....0..0..1....0..0..1....0..1..0....0..1..0
..1..0..0....0..0..0....0..1..1....0..0..0....0..1..1....0..0..0....1..0..0
..1..0..1....0..1..1....1..0..1....1..1..1....0..0..0....1..1..1....1..0..1
..1..1..1....0..1..1....0..1..0....0..0..0....0..1..0....1..0..0....1..1..0

R. H. Hardin, Table of n, a(n) for n = 1..631

Column 2 is A004171(n-1)

Row 2 is A104934

A302069 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 25, 32, 8, 16, 81, 148, 128, 16, 32, 263, 748, 884, 512, 32, 64, 855, 3657, 7070, 5296, 2048, 64, 128, 2778, 18108, 54177, 67070, 31760, 8192, 128, 256, 9027, 89658, 420121, 807601, 636852, 190528, 32768, 256, 512, 29333, 444359

Offset: 1

R. H. Hardin, Mar 31 2018

Table starts
...1......2.......4.........8..........16............32..............64
...2......8......25........81.........263...........855............2778
...4.....32.....148.......748........3657.........18108...........89658
...8....128.....884......7070.......54177........420121.........3247765
..16....512....5296.....67070......807601.......9825815.......119508742
..32...2048...31760....636852....12063625.....230634314......4418931065
..64...8192..190528...6048836...180330117....5420105343....163660519064
.128..32768.1143104..57457232..2696254757..127431664603...6065045335103
.256.131072.6858496.545796112.40316943551.2996509042607.224815724811979

			Some solutions for n=5 k=4
..0..1..0..0. .0..1..0..0. .0..0..1..1. .0..1..1..0. .0..1..0..0
..1..0..0..0. .1..1..1..0. .0..1..0..0. .1..0..1..0. .0..1..1..1
..1..0..1..0. .0..1..1..0. .0..0..1..0. .0..1..0..1. .1..0..1..0
..1..1..1..0. .0..0..1..0. .1..1..1..0. .1..0..1..0. .0..0..1..0
..1..1..0..1. .1..0..1..1. .1..1..0..1. .0..0..0..1. .0..0..1..0

R. H. Hardin, Table of n, a(n) for n = 1..311

Column 1 is A000079(n-1).
Column 2 is A004171(n-1).
Row 1 is A000079(n-1).
Row 2 is A301842.

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 8*a(n-1) -12*a(n-2) for n>3
k=4: a(n) = 16*a(n-1) -76*a(n-2) +148*a(n-3) -124*a(n-4) +36*a(n-5) for n>6
k=5: [order 11] for n>13
k=6: [order 25] for n>27
k=7: [order 53] for n>56
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4) for n>6
n=3: [order 15] for n>18
n=4: [order 53] for n>58

A302741 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 228, 128, 16, 32, 512, 1637, 1652, 512, 32, 64, 2048, 11814, 21625, 11980, 2048, 64, 128, 8192, 85268, 285613, 286631, 86916, 8192, 128, 256, 32768, 615589, 3778433, 6947036, 3798398, 630604, 32768, 256, 512, 131072

Offset: 1

R. H. Hardin, Apr 12 2018

Table starts
...1......2........4..........8............16..............32
...2......8.......32........128...........512............2048
...4.....32......228.......1637.........11814...........85268
...8....128.....1652......21625........285613.........3778433
..16....512....11980.....286631.......6947036.......168799572
..32...2048....86916....3798398.....168833401......7530280825
..64...8192...630604...50347423....4104946296....336148647504
.128..32768..4575332..667361051...99807877377..15005851329729
.256.131072.33196332.8845980434.2426739457531.669868217032865

			Some solutions for n=5 k=4
..0..0..1..0. .0..0..1..0. .0..0..1..0. .0..0..0..1. .0..0..1..0
..0..0..0..0. .0..0..1..0. .0..0..0..0. .0..1..0..1. .0..1..0..1
..0..1..1..1. .0..1..1..0. .0..1..1..1. .0..1..0..0. .0..0..1..0
..1..0..0..0. .1..1..0..1. .0..0..1..0. .1..1..0..0. .1..1..1..1
..0..0..1..0. .1..1..0..1. .0..0..1..1. .0..1..1..1. .1..1..0..0

R. H. Hardin, Table of n, a(n) for n = 1..180

Column 1 is A000079(n-1).
Column 2 is A004171(n-1).
Row 1 is A000079(n-1).
Row 2 is A004171(n-1).

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 7*a(n-1) +2*a(n-2) +2*a(n-3) -20*a(n-4) -16*a(n-5)
k=4: [order 15]
k=5: [order 46]
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 4*a(n-1)
n=3: a(n) = 7*a(n-1) +4*a(n-2) -17*a(n-3) -3*a(n-4) -9*a(n-6) +14*a(n-7) for n>8
n=4: [order 15] for n>16
n=5: [order 64] for n>65

A302808 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 29, 32, 8, 16, 105, 169, 128, 16, 32, 384, 934, 1010, 512, 32, 64, 1405, 5117, 8718, 6084, 2048, 64, 128, 5135, 28128, 74072, 82367, 36456, 8192, 128, 256, 18766, 154494, 632004, 1089773, 773520, 218640, 32768, 256, 512, 68589, 848519

Offset: 1

R. H. Hardin, Apr 13 2018

Table starts
...1......2.......4.........8..........16............32..............64
...2......8......29.......105.........384..........1405............5135
...4.....32.....169.......934........5117.........28128..........154494
...8....128....1010......8718.......74072........632004.........5396562
..16....512....6084.....82367.....1089773......14458177.......192211013
..32...2048...36456....773520....15904814.....327603711......6769884156
..64...8192..218640...7267160...232260380....7428713676....238687785290
.128..32768.1312416..68346451..3396923500..168777255305...8434497360938
.256.131072.7873344.642498696.49653502029.3832039683236.297820640670676

			Some solutions for n=5 k=4
..0..1..0..0. .0..0..0..0. .0..0..1..0. .0..0..1..0. .0..1..1..0
..1..0..1..1. .0..1..1..0. .1..0..1..0. .0..0..1..1. .1..1..1..1
..1..0..1..0. .0..1..0..1. .1..0..1..1. .0..0..1..1. .0..0..0..0
..0..1..0..1. .0..0..0..0. .1..0..0..0. .1..0..1..1. .0..1..1..0
..1..1..0..0. .0..0..1..1. .1..0..1..0. .1..0..1..0. .1..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..180

Column 1 is A000079(n-1).
Column 2 is A004171(n-1).
Row 1 is A000079(n-1).
Row 2 is A302266.

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 6*a(n-1) +24*a(n-3) -144*a(n-4) for n>6
k=4: [order 18] for n>20
k=5: [order 90] for n>92
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4)
n=3: [order 13] for n>15
n=4: [order 48] for n>50

A302965 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 29, 32, 8, 16, 105, 154, 128, 16, 32, 384, 786, 833, 512, 32, 64, 1405, 3924, 6206, 4527, 2048, 64, 128, 5135, 19868, 43588, 49521, 24602, 8192, 128, 256, 18766, 100161, 314989, 493132, 395493, 133757, 32768, 256, 512, 68589, 505908

Offset: 1

R. H. Hardin, Apr 16 2018

Table starts
...1......2.......4.........8.........16...........32.............64
...2......8......29.......105........384.........1405...........5135
...4.....32.....154.......786.......3924........19868.........100161
...8....128.....833......6206......43588.......314989........2257439
..16....512....4527.....49521.....493132......5122000.......52646395
..32...2048...24602....395493....5602382.....83644490.....1233435694
..64...8192..133757...3157171...63612987...1365216668....28906043997
.128..32768..727293..25208524..722646394..22301032112...677939939546
.256.131072.3954552.201291251.8212135689.364489574945.15913688413086

			Some solutions for n=5 k=4
..0..1..0..1. .0..1..1..0. .0..0..0..1. .0..0..1..0. .0..0..1..0
..1..1..0..0. .0..0..0..0. .0..0..1..1. .1..0..1..1. .1..0..1..0
..0..1..0..0. .1..1..1..1. .1..0..1..1. .0..1..0..0. .1..0..1..0
..1..1..1..1. .1..0..0..1. .1..0..1..0. .0..1..0..0. .1..0..1..1
..1..0..0..0. .1..0..1..0. .1..0..1..0. .0..1..0..1. .0..1..0..0

R. H. Hardin, Table of n, a(n) for n = 1..180

Column 1 is A000079(n-1).
Column 2 is A004171(n-1).
Row 1 is A000079(n-1).
Row 2 is A302266.

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 7*a(n-1) -7*a(n-2) -56*a(n-4) +64*a(n-5) for n>6
k=4: [order 19] for n>20
k=5: [order 80] for n>81
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4)
n=3: [order 12] for n>13
n=4: [order 44] for n>45

cp's OEIS Frontend

A220579 T(n,k)=Equals one maps: number of nXk binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 nXk array.

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A301841 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

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A302265 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A013776 a(n) = 2^(4*n+1).

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GAP

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A028403 Number of types of Boolean functions of n variables under a certain group.

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Magma

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A208709 T(n,k)=Number of nXk 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

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A302069 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

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A302741 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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