A281056 -id:A281056 - cp's OEIS frontend

A281050 Number of n X 2 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

0, 1, 6, 29, 122, 468, 1686, 5807, 19338, 62731, 199264, 622152, 1914780, 5821645, 17515566, 52221929, 154461110, 453654108, 1324053522, 3842768987, 11096398578, 31895230903, 91296545404, 260329675536, 739725018360, 2095147333465

Offset: 1

R. H. Hardin, Jan 13 2017

nonn

			Some solutions for n=4:
..0..0. .0..0. .0..1. .0..0. .0..0. .0..1. .0..0. .0..0. .0..0. .0..0
..0..0. .1..1. .1..1. .0..0. .0..1. .1..1. .1..1. .1..1. .0..0. .0..1
..1..0. .1..1. .0..0. .1..0. .0..1. .1..0. .0..0. .1..1. .1..1. .1..1
..0..1. .0..0. .0..1. .1..0. .1..1. .1..0. .0..0. .0..1. .0..1. .0..0

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

Column 2 of A281056.

Empirical: a(n) = 9*a(n-1) - 30*a(n-2) + 45*a(n-3) - 30*a(n-4) + 9*a(n-5) - a(n-6).

Empirical g.f.: x^2*(1 - 3*x + 5*x^2 - 4*x^3) / (1 - 3*x + x^2)^3. - Colin Barker, Feb 15 2019

A281051 Number of n X 3 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 6, 68, 376, 1492, 4988, 15028, 42252, 113076, 291660, 731060, 1791052, 4306868, 10197068, 23828404, 55060556, 125999028, 285894732, 643864500, 1440442444, 3203438516, 7086237772, 15599703988, 34190878796, 74638727092, 162339448908

Offset: 1

R. H. Hardin, Jan 13 2017

nonn

			Some solutions for n=4:
..0..0..1. .0..1..0. .0..0..0. .0..1..0. .0..1..1. .0..1..0. .0..1..0
..1..0..0. .0..1..1. .1..0..1. .0..0..1. .0..0..0. .0..1..0. .0..1..0
..0..1..0. .1..0..0. .1..0..0. .1..1..1. .0..1..1. .1..0..0. .1..0..0
..0..0..1. .0..1..1. .1..1..0. .1..0..1. .1..0..0. .1..1..1. .1..0..1

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

Column 3 of A281056.

Empirical: a(n) = 5*a(n-1) - 6*a(n-2) - 4*a(n-3) + 8*a(n-4) for n>6.

Empirical g.f.: 2*x^2*(3 + x)*(1 + 2*x)*(1 + 4*x + 2*x^2) / ((1 + x)*(1 - 2*x)^3). - Colin Barker, Feb 15 2019

A281052 Number of nX4 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

1, 34, 239, 1022, 3416, 10112, 27635, 71419, 177320, 426696, 1002035, 2306828, 5224307, 11669686, 25762564, 56301813, 121961820, 262154625, 559637795, 1187392495, 2505484374, 5260557953, 10995496220, 22888340830, 47465895442

Offset: 1

R. H. Hardin, Jan 13 2017

nonn

Column 4 of A281056.

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

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

Cf. A281056.

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

A281053 Number of nX5 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

2, 104, 618, 2452, 7803, 22106, 58005, 144283, 344972, 800225, 1812024, 4023754, 8791481, 18948288, 40366695, 85135873, 177990242, 369259703, 760850914, 1558181104, 3173635543, 6432024694, 12977428633, 26076680087, 52202242904

Offset: 1

R. H. Hardin, Jan 13 2017

nonn

Column 5 of A281056.

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

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

Cf. A281056.

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

A281054 Number of nX6 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

6, 251, 1403, 5400, 16875, 46610, 119205, 288527, 671451, 1515524, 3339671, 7217269, 15347530, 32196671, 66765699, 137073842, 278977066, 563443975, 1130260537, 2253558987, 4468793135, 8818038639, 17322550753, 33890757331

Offset: 1

R. H. Hardin, Jan 13 2017

nonn

Column 6 of A281056.

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

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

Cf. A281056.

Empirical: a(n) = 3*a(n-1) +3*a(n-2) -11*a(n-3) -9*a(n-4) +15*a(n-5) +20*a(n-6) +3*a(n-7) -18*a(n-8) -27*a(n-9) -9*a(n-10) +15*a(n-11) +20*a(n-12) +12*a(n-13) -7*a(n-15) -6*a(n-16) -3*a(n-17) -a(n-18) for n>21

A281055 Number of nX7 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

13, 535, 2828, 10570, 32370, 87995, 221212, 526340, 1201939, 2661939, 5752796, 12190173, 25413086, 52258597, 106216045, 213723050, 426288170, 843735147, 1658596579, 3240610144, 6297012052, 12175728717, 23437264280, 44930659786

Offset: 1

R. H. Hardin, Jan 13 2017

nonn

Column 7 of A281056.

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

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

Cf. A281056.

Empirical: a(n) = 5*a(n-1) -6*a(n-2) -4*a(n-3) +5*a(n-4) +9*a(n-5) -3*a(n-6) -3*a(n-7) -3*a(n-8) -9*a(n-9) +6*a(n-11) +8*a(n-12) +2*a(n-13) +3*a(n-14) -3*a(n-15) -3*a(n-16) -3*a(n-17) -a(n-18) -a(n-19) for n>23

A281057 Number of 2 X n 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 1, 6, 34, 104, 251, 535, 1076, 2090, 3956, 7353, 13474, 24417, 43846, 78142, 138374, 243687, 427098, 745403, 1296072, 2246018, 3880504, 6686165, 11491746, 19706373, 33722458, 57596214, 98195818, 167136611, 284039674, 482013727, 816869276

Offset: 1

R. H. Hardin, Jan 13 2017

nonn

			Some solutions for n=4:
..0..0..0..1. .0..1..1..1. .0..1..1..0. .0..0..1..1. .0..1..0..0
..0..1..1..0. .0..0..1..0. .0..0..0..0. .1..1..0..1. .0..0..1..0

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

Row 2 of A281056.

Empirical: a(n) = 5*a(n-1) - 7*a(n-2) - 2*a(n-3) + 10*a(n-4) - 2*a(n-5) - 5*a(n-6) + a(n-7) + a(n-8) for n>14.

Empirical g.f.: x^2*(1 + x + 11*x^2 - 22*x^3 - 29*x^4 + 18*x^5 + 43*x^6 + 14*x^7 - 31*x^8 - 13*x^9 + 8*x^10 + 2*x^11 - x^12) / ((1 - x)^2*(1 - x - x^2)^3). - Colin Barker, Feb 15 2019

A281058 Number of 3 X n 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 6, 68, 239, 618, 1403, 2828, 5482, 10342, 19136, 34907, 62976, 112617, 199929, 352771, 619208, 1081946, 1882951, 3265367, 5644772, 9730124, 16728760, 28693405, 49108842, 83882613, 143016171, 243420929, 413658928, 701916100, 1189400585

Offset: 1

R. H. Hardin, Jan 13 2017

nonn

			Some solutions for n=4:
..0..1..0..0. .0..1..0..0. .0..1..1..0. .0..0..0..0. .0..0..1..1
..0..1..0..1. .0..1..0..0. .1..0..1..1. .1..0..1..0. .1..0..1..0
..0..1..1..0. .0..1..1..0. .1..0..1..0. .1..0..1..1. .1..0..0..1

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

Row 3 of A281056.

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

Empirical g.f.: x^2*(6 + 38*x - 59*x^2 - 89*x^3 + 62*x^4 - 51*x^5 + 175*x^6 + 166*x^7 - 217*x^8 - 106*x^9 + 71*x^10 + 21*x^11 - 7*x^12 - x^13) / ((1 - x)^2*(1 - x - x^2)^3). - Colin Barker, Feb 15 2019

A281059 Number of 4Xn 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 29, 376, 1022, 2452, 5400, 10570, 19892, 36616, 66354, 118926, 211382, 373266, 655580, 1146156, 1995858, 3463242, 5990498, 10332426, 17775144, 30506480, 52242450, 89285638, 152311246, 259377954, 440998484, 748670868, 1269219570

Offset: 1

R. H. Hardin, Jan 13 2017

nonn

Row 4 of A281056.

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

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

Cf. A281056.

Empirical: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>17

A281060 Number of 5Xn 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 122, 1492, 3416, 7803, 16875, 32370, 59669, 107693, 191953, 339219, 595824, 1041681, 1814253, 3149435, 5451162, 9409735, 16202663, 27835100, 47716151, 81633286, 139397983, 237621979, 404396106, 687167939, 1165993033, 1975805797

Offset: 1

R. H. Hardin, Jan 13 2017

nonn

Row 5 of A281056.

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

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

Cf. A281056.

Empirical: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>18

cp's OEIS Frontend

A281050 Number of n X 2 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A281051 Number of n X 3 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A281052 Number of nX4 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A281053 Number of nX5 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A281054 Number of nX6 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A281055 Number of nX7 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A281057 Number of 2 X n 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A281058 Number of 3 X n 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A281059 Number of 4Xn 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A281060 Number of 5Xn 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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