A303314 -id:A303314 - cp's OEIS frontend

A303308 Number of n X n 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 3, 12, 36, 139, 1221, 26184, 746323, 23967605, 1285074158, 140135122490, 23444843868325, 5152091496332058, 1785689257359207106, 1097023324108868377427, 1066418515771155179484946

Offset: 1

R. H. Hardin, Apr 21 2018

nonn

Diagonal of A303314.

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

R. H. Hardin, Table of n, a(n) for n = 1..17

Cf. A303314.

A303309 Number of nX3 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

3, 3, 12, 11, 19, 34, 53, 83, 136, 223, 359, 578, 937, 1519, 2456, 3971, 6427, 10402, 16829, 27227, 44056, 71287, 115343, 186626, 301969, 488599, 790568, 1279163, 2069731, 3348898, 5418629, 8767523, 14186152, 22953679, 37139831, 60093506

Offset: 1

R. H. Hardin, Apr 21 2018

nonn

Column 3 of A303314.

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

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

Cf. A303314.

Empirical: a(n) = a(n-1) +a(n-3) +a(n-4) for n>7

A303310 Number of nX4 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

5, 5, 17, 36, 74, 165, 361, 783, 1710, 3744, 8176, 17851, 39009, 85239, 186206, 406800, 888794, 1941803, 4242301, 9268393, 20249240, 44239542, 96652372, 211161719, 461336399, 1007905991, 2202025876, 4810883806, 10510594448, 22963055655

Offset: 1

R. H. Hardin, Apr 21 2018

nonn

Column 4 of A303314.

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

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

Cf. A303314.

Empirical: a(n) = a(n-1) +a(n-2) +3*a(n-3) +2*a(n-4) -a(n-5) -2*a(n-6) -a(n-7) for n>10

A303311 Number of nX5 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

8, 7, 24, 50, 139, 349, 853, 2180, 5525, 13824, 34900, 88161, 221923, 559409, 1411020, 3556271, 8964218, 22600998, 56974213, 143622769, 362071261, 912756908, 2300972077, 5800604608, 14622927344, 36863258801, 92929626827, 234268970653

Offset: 1

R. H. Hardin, Apr 21 2018

nonn

Column 5 of A303314.

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

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

Cf. A303314.

Empirical: a(n) = a(n-1) +9*a(n-3) +2*a(n-4) +4*a(n-5) -10*a(n-6) -6*a(n-7) +4*a(n-9) for n>12

A303312 Number of nX6 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

13, 13, 67, 128, 410, 1221, 3453, 10223, 30247, 88071, 257997, 758575, 2222443, 6510901, 19099863, 56003627, 164158635, 481322825, 1411283805, 4137560893, 12130815503, 35567022201, 104278542849, 305732562651, 896380484697

Offset: 1

R. H. Hardin, Apr 21 2018

nonn

Column 6 of A303314.

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

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

Cf. A303314.

Empirical: a(n) = a(n-1) +2*a(n-2) +10*a(n-3) +6*a(n-4) -5*a(n-5) -15*a(n-6) -8*a(n-7) -4*a(n-8) for n>11

A303313 Number of nX7 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

21, 23, 158, 439, 1799, 7096, 26184, 100128, 387892, 1473950, 5617780, 21537368, 82283698, 314136752, 1201134460, 4591062616, 17541004106, 67038118694, 256214474112, 979116873266, 3741800363318, 14300090089956, 54649561868376

Offset: 1

R. H. Hardin, Apr 21 2018

nonn

Column 7 of A303314.

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

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

Cf. A303314.

Empirical: a(n) = a(n-1) +a(n-2) +36*a(n-3) +23*a(n-4) +15*a(n-5) -252*a(n-6) -288*a(n-7) -81*a(n-8) +830*a(n-9) +496*a(n-10) +172*a(n-11) -720*a(n-12) -184*a(n-13) -396*a(n-14) +352*a(n-15) -248*a(n-16) +112*a(n-17) -176*a(n-18) -64*a(n-20) for n>23

A303315 Number of 3Xn 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

4, 4, 12, 17, 24, 67, 158, 298, 595, 1337, 2863, 5840, 12231, 26168, 55140, 115193, 242621, 512713, 1078852, 2267487, 4776110, 10063518, 21181387, 44579665, 93874659, 197672892, 416137435, 876080072, 1844597384, 3883701257, 8176491213

Offset: 1

R. H. Hardin, Apr 21 2018

nonn

Row 3 of A303314.

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

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

Cf. A303314.

Empirical: a(n) = a(n-1) +3*a(n-3) +4*a(n-4) for n>7

A303316 Number of 4Xn 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

8, 6, 11, 36, 50, 128, 439, 1085, 2431, 6452, 17455, 43514, 108524, 281615, 726261, 1839731, 4685152, 12025643, 30754258, 78396104, 200278695, 512290781, 1308785863, 3342222476, 8540451095, 21826102586, 55761123412, 142456533311

Offset: 1

R. H. Hardin, Apr 21 2018

nonn

Row 4 of A303314.

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

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

Cf. A303314.

Empirical: a(n) = a(n-1) +a(n-2) +5*a(n-3) +9*a(n-4) -3*a(n-5) -7*a(n-6) -2*a(n-7) for n>11

A303317 Number of 5Xn 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

16, 9, 19, 74, 139, 410, 1799, 5907, 16494, 53290, 184915, 593160, 1846238, 5986532, 19644799, 63120477, 201894029, 652765881, 2113653016, 6806905917, 21913260238, 70736938785, 228339832475, 736091706666, 2373144545904, 7656031069031

Offset: 1

R. H. Hardin, Apr 21 2018

nonn

Row 5 of A303314.

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

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

Cf. A303314.

Empirical: a(n) = 2*a(n-1) -a(n-2) +11*a(n-3) +21*a(n-4) -13*a(n-5) +5*a(n-6) -37*a(n-7) -34*a(n-8) +4*a(n-9) -20*a(n-10) +18*a(n-11) -7*a(n-12) for n>16

A303318 Number of 6Xn 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

32, 14, 34, 165, 349, 1221, 7096, 30280, 102683, 403872, 1783894, 7248640, 27856927, 111871711, 461547267, 1859721535, 7397094062, 29793428041, 120739708314, 486065859963, 1951092593903, 7859276232228, 31701254570200, 127635189909079

Offset: 1

R. H. Hardin, Apr 21 2018

nonn

Row 6 of A303314.

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

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

Cf. A303314.

Empirical: a(n) = a(n-1) +3*a(n-2) +18*a(n-3) +87*a(n-4) +23*a(n-5) -149*a(n-6) -305*a(n-7) -678*a(n-8) -45*a(n-9) +981*a(n-10) +937*a(n-11) +1834*a(n-12) +317*a(n-13) -1968*a(n-14) -1457*a(n-15) -2157*a(n-16) -964*a(n-17) +830*a(n-18) +254*a(n-19) +161*a(n-20) +152*a(n-21) -15*a(n-22) -3*a(n-23) for n>28

cp's OEIS Frontend

A303308 Number of n X n 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A303309 Number of nX3 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A303310 Number of nX4 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A303311 Number of nX5 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A303312 Number of nX6 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A303313 Number of nX7 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A303315 Number of 3Xn 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A303316 Number of 4Xn 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A303317 Number of 5Xn 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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