A219142 -id:A219142 - cp's OEIS frontend

A219136 Unchanging value maps: number of n X 2 binary arrays indicating the locations of corresponding elements unequal to no horizontal, diagonal or antidiagonal neighbor in a random 0..2 n X 2 array.

2, 6, 18, 51, 142, 405, 1157, 3289, 9344, 26580, 75621, 215076, 611683, 1739781, 4948421, 14074414, 40030688, 113856507, 323834334, 921058929, 2619701953, 7451032833, 21192445976, 60276171664, 171439240421, 487612482144

Offset: 1

R. H. Hardin, Nov 12 2012

nonn

Column 2 of A219142.

			Some solutions for n=3:
..1..0....0..0....0..0....0..0....1..1....0..0....0..0....0..0....1..1....0..0
..0..0....1..0....0..0....0..0....0..1....0..1....1..0....0..1....1..0....0..0
..0..1....1..1....1..0....0..0....0..0....0..0....0..0....1..1....0..0....1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A219142.

Empirical: a(n) = 2*a(n-1) + a(n-2) + 3*a(n-3) + 4*a(n-4) - 2*a(n-5) - 4*a(n-6).

Empirical g.f.: x*(2 + 2*x + 4*x^2 + 3*x^3 - 4*x^4 - 4*x^5) / ((1 + 2*x^2)*(1 - 2*x - 3*x^2 + x^3 + 2*x^4)). - Colin Barker, Mar 10 2018

A219143 Unchanging value maps: number of 2 X n binary arrays indicating the locations of corresponding elements unequal to no horizontal, diagonal or antidiagonal neighbor in a random 0..2 2 X n array.

Original entry on oeis.org

1, 6, 18, 39, 96, 225, 543, 1293, 3096, 7392, 17673, 42228, 100929, 241197, 576441, 1377606, 3292314, 7868187, 18803964, 44939013, 107398431, 256668285, 613403916, 1465955712, 3503443917, 8372776200, 20009848437, 47820940581, 114285841233

Offset: 1

R. H. Hardin, Nov 12 2012

nonn

Row 2 of A219142.

			Some solutions for n=3:
..1..0..0....0..0..0....0..0..1....0..0..1....0..0..1....1..0..1....1..1..1
..0..0..1....1..0..0....1..0..0....1..0..1....0..0..0....0..0..0....1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A219142.

Empirical: a(n) = 2*a(n-1) + a(n-2) - a(n-3) + 2*a(n-4) for n>5.

Empirical g.f.: x*(1 + 4*x + 5*x^2 - 2*x^3 + 4*x^4) / (1 - 2*x - x^2 + x^3 - 2*x^4). - Colin Barker, Mar 11 2018

A219144 Unchanging value maps: number of 3Xn binary arrays indicating the locations of corresponding elements unequal to no horizontal, diagonal or antidiagonal neighbor in a random 0..2 3Xn array.

Original entry on oeis.org

1, 18, 78, 281, 1072, 4033, 15255, 57963, 220068, 835820, 3172817, 12044346, 45722019, 173574485, 658947323, 2501581220, 9496787730, 36052730049, 136867284190, 519590670019, 1972527813429, 7488329193659, 28428025632710

Offset: 1

R. H. Hardin Nov 12 2012

nonn

Row 3 of A219142

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

R. H. Hardin, Table of n, a(n) for n = 1..40

Empirical: a(n) = 4*a(n-1) -8*a(n-3) +17*a(n-4) +17*a(n-5) -29*a(n-6) -13*a(n-7) +9*a(n-8) -31*a(n-9) -26*a(n-10) +30*a(n-11) -3*a(n-12) +6*a(n-13) +17*a(n-14) -3*a(n-15) +3*a(n-16) -2*a(n-17) for n>18

A219137 Unchanging value maps: number of n X 3 binary arrays indicating the locations of corresponding elements unequal to no horizontal, diagonal or antidiagonal neighbor in a random 0..2 n X 3 array.

Original entry on oeis.org

4, 18, 78, 331, 1400, 5949, 25277, 107353, 455938, 1936500, 8224877, 34933256, 148370893, 630171269, 2676507659, 11367850562, 48282330086, 205068091043, 870979546682, 3699285278069, 15711863292777, 66732525229601

Offset: 1

R. H. Hardin, Nov 12 2012

nonn

Column 3 of A219142.

			Some solutions for n=3:
..0..0..0....1..0..0....0..0..0....0..0..0....0..0..1....0..0..0....0..0..1
..1..0..1....1..0..1....0..0..1....0..1..0....0..0..1....0..0..0....1..0..0
..0..0..0....1..1..1....1..0..0....1..1..1....0..0..0....0..0..1....0..0..1

R. H. Hardin, Table of n, a(n) for n = 1..106

Cf. A219142.

Empirical: a(n) = 4*a(n-1) + a(n-2) + a(n-3) - 12*a(n-5) - 10*a(n-6) + 2*a(n-7) + 4*a(n-8).

Empirical g.f.: x*(4 + 2*x + 2*x^2 - 3*x^3 - 20*x^4 - 12*x^5 + 6*x^6 + 4*x^7) / (1 - 4*x - x^2 - x^3 + 12*x^5 + 10*x^6 - 2*x^7 - 4*x^8). - Colin Barker, Jul 25 2018

A219138 Unchanging value maps: number of nX4 binary arrays indicating the locations of corresponding elements unequal to no horizontal, diagonal or antidiagonal neighbor in a random 0..2 nX4 array.

Original entry on oeis.org

7, 39, 281, 1774, 11385, 73136, 472638, 3050285, 19667721, 126807809, 817795362, 5274346426, 34015377046, 219367395594, 1414720693245, 9123720789554, 58840106012423, 379467286876826, 2447231592206585, 15782503349398343

Offset: 1

R. H. Hardin Nov 12 2012

nonn

Column 4 of A219142

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

R. H. Hardin, Table of n, a(n) for n = 1..31

A219140 Unchanging value maps: number of nX6 binary arrays indicating the locations of corresponding elements unequal to no horizontal, diagonal or antidiagonal neighbor in a random 0..2 nX6 array.

Original entry on oeis.org

21, 225, 4033, 59127, 872437, 12867295, 191707377, 2851740545, 42351530487, 628917557052, 9343657589877, 138832484811480, 2062679454951201, 30644671161036036, 455284849342096283, 6764205083943142280

Offset: 1

R. H. Hardin Nov 12 2012

nonn

Column 6 of A219142

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

R. H. Hardin, Table of n, a(n) for n = 1..31

A219141 Unchanging value maps: number of nX7 binary arrays indicating the locations of corresponding elements unequal to no horizontal, diagonal or antidiagonal neighbor in a random 0..2 nX7 array.

Original entry on oeis.org

37, 543, 15255, 341648, 7640541, 170792866, 3862325048, 87205791997, 1964627314453, 44248075120119, 997182574575448, 22477181379388546, 506606543634822152, 11417623925479199496, 257329160512779838675

Offset: 1

R. H. Hardin Nov 12 2012

nonn

Column 7 of A219142

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

R. H. Hardin, Table of n, a(n) for n = 1..21

A219135 Unchanging value maps: number of n X n binary arrays indicating the locations of corresponding elements unequal to no horizontal, diagonal or antidiagonal neighbor in a random 0..2 n X n array.

Original entry on oeis.org

1, 6, 78, 1774, 101600, 12867295, 3862325048, 2678391894154

Offset: 1

R. H. Hardin Nov 12 2012

nonn

Diagonal of A219142

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

A219139 Unchanging value maps: number of nX5 binary arrays indicating the locations of corresponding elements unequal to no horizontal, diagonal or antidiagonal neighbor in a random 0..2 nX5 array.

Original entry on oeis.org

12, 96, 1072, 10505, 101600, 989947, 9702349, 94937311, 927766394, 9067631046, 88653591037, 866785617482, 8474253980191, 82848823383647, 809985234784217

Offset: 1

R. H. Hardin Nov 12 2012

nonn

Column 5 of A219142

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

A219145 Unchanging value maps: number of 4Xn binary arrays indicating the locations of corresponding elements unequal to no horizontal, diagonal or antidiagonal neighbor in a random 0..2 4Xn array.

Original entry on oeis.org

1, 51, 331, 1774, 10505, 59127, 341648, 1963817, 11341895, 65406069, 377314947, 2175983774, 12550566460, 72389111386, 417539600863, 2408347532016, 13891206637891

Offset: 1

R. H. Hardin Nov 12 2012

nonn

Row 4 of A219142

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

cp's OEIS Frontend

A219136 Unchanging value maps: number of n X 2 binary arrays indicating the locations of corresponding elements unequal to no horizontal, diagonal or antidiagonal neighbor in a random 0..2 n X 2 array.

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A219143 Unchanging value maps: number of 2 X n binary arrays indicating the locations of corresponding elements unequal to no horizontal, diagonal or antidiagonal neighbor in a random 0..2 2 X n array.

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A219144 Unchanging value maps: number of 3Xn binary arrays indicating the locations of corresponding elements unequal to no horizontal, diagonal or antidiagonal neighbor in a random 0..2 3Xn array.

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A219137 Unchanging value maps: number of n X 3 binary arrays indicating the locations of corresponding elements unequal to no horizontal, diagonal or antidiagonal neighbor in a random 0..2 n X 3 array.

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A219138 Unchanging value maps: number of nX4 binary arrays indicating the locations of corresponding elements unequal to no horizontal, diagonal or antidiagonal neighbor in a random 0..2 nX4 array.

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A219140 Unchanging value maps: number of nX6 binary arrays indicating the locations of corresponding elements unequal to no horizontal, diagonal or antidiagonal neighbor in a random 0..2 nX6 array.

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A219141 Unchanging value maps: number of nX7 binary arrays indicating the locations of corresponding elements unequal to no horizontal, diagonal or antidiagonal neighbor in a random 0..2 nX7 array.

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A219135 Unchanging value maps: number of n X n binary arrays indicating the locations of corresponding elements unequal to no horizontal, diagonal or antidiagonal neighbor in a random 0..2 n X n array.

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A219139 Unchanging value maps: number of nX5 binary arrays indicating the locations of corresponding elements unequal to no horizontal, diagonal or antidiagonal neighbor in a random 0..2 nX5 array.

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A219145 Unchanging value maps: number of 4Xn binary arrays indicating the locations of corresponding elements unequal to no horizontal, diagonal or antidiagonal neighbor in a random 0..2 4Xn array.

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