A208269 -id:A208269 - cp's OEIS frontend

A208263 Number of n X n 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 left-upward diagonal neighbors.

1, 7, 161, 11929, 2867739, 2234126207, 5641457245533, 46171961042899417, 1224814800337927770335, 105309458529148583423889079, 29347371781481633173790977728301, 26507936613513086328494176843991041391

Offset: 1

R. H. Hardin Feb 24 2012

nonn

Diagonal of A208269

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

R. H. Hardin, Table of n, a(n) for n = 1..19

A208264 Number of n X 3 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 left-upward diagonal neighbors.

Original entry on oeis.org

4, 25, 161, 1033, 6631, 42563, 273205, 1753657, 11256431, 72253147, 463780861, 2976931745, 19108426759, 122653794067, 787294181189, 5053509615817, 32437632650335, 208211736387083, 1336476297041869, 8578617726111793

Offset: 1

R. H. Hardin, Feb 24 2012

nonn

Column 3 of A208269.

			Some solutions for n=4:
..0..1..0....0..0..1....0..1..1....0..1..1....0..0..0....0..0..0....0..0..1
..0..0..0....0..1..0....1..1..0....0..1..0....1..0..1....0..1..1....0..1..1
..1..1..1....1..1..1....0..1..0....0..1..1....1..0..1....1..0..1....1..0..0
..1..0..0....0..0..0....0..1..0....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. A208269.

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

Empirical g.f.: x*(4 + x - x^2) / (1 - 6*x - 3*x^2 + 2*x^3). - Colin Barker, Jun 29 2018

A208265 Number of n X 4 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 left-upward diagonal neighbors.

Original entry on oeis.org

8, 89, 1033, 11929, 137845, 1592731, 18403423, 212644499, 2457026181, 28390000737, 328035635669, 3790326714043, 43795780208895, 506043544208099, 5847140236199813, 67561476345437377, 780647102957445445

Offset: 1

R. H. Hardin, Feb 24 2012

nonn

Column 4 of A208269.

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

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

Cf. A208269.

Empirical: a(n) = 10*a(n-1) + 20*a(n-2) - 21*a(n-3) - 30*a(n-4) + 8*a(n-5).

Empirical g.f.: x*(8 + 9*x - 17*x^2 - 13*x^3 + 4*x^4) / (1 - 10*x - 20*x^2 + 21*x^3 + 30*x^4 - 8*x^5). - Colin Barker, Jun 29 2018

A208266 Number of nX5 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 left-upward diagonal neighbors.

Original entry on oeis.org

16, 317, 6631, 137845, 2867739, 59655167, 1240971177, 25815151595, 537016650729, 11171225344081, 232388094425359, 4834225856311743, 100563411775559793, 2091958482792842737, 43517718984137019457, 905272203611654999429

Offset: 1

R. H. Hardin Feb 24 2012

nonn

Column 5 of A208269

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

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

Empirical: a(n) = 21*a(n-1) +9*a(n-2) -278*a(n-3) +73*a(n-4) +790*a(n-5) -662*a(n-6) +29*a(n-7) +69*a(n-8) -10*a(n-9)

A208267 Number of nX6 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 left-upward diagonal neighbors.

Original entry on oeis.org

32, 1129, 42563, 1592731, 59655167, 2234126207, 83670667271, 3133560234217, 117355367786585, 4395090865370635, 164601109918978615, 6164497208894901477, 230867373009598884627, 8646243499452479433569, 323811570588787197424201

Offset: 1

R. H. Hardin Feb 24 2012

nonn

Column 6 of A208269

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

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

Empirical: a(n) = 36*a(n-1) +120*a(n-2) -2391*a(n-3) -3905*a(n-4) +50702*a(n-5) +27152*a(n-6) -396016*a(n-7) +154999*a(n-8) +751787*a(n-9) -499260*a(n-10) -410368*a(n-11) +355981*a(n-12) +38077*a(n-13) -70276*a(n-14) +6203*a(n-15) +3386*a(n-16) -622*a(n-17) +28*a(n-18)

A208268 Number of nX7 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 left-upward diagonal neighbors.

Original entry on oeis.org

64, 4021, 273205, 18403423, 1240971177, 83670667271, 5641457245533, 380372051615157, 25646375739266275, 1729192685453990877, 116589859961103508219, 7861006788319434001589, 530024032549172830292655

Offset: 1

R. H. Hardin Feb 24 2012

nonn

Column 7 of A208269

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

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

Empirical: a(n) = 77*a(n-1) -429*a(n-2) -16791*a(n-3) +132938*a(n-4) +1140609*a(n-5) -11250708*a(n-6) -21101443*a(n-7) +356560316*a(n-8) -276630106*a(n-9) -3595865197*a(n-10) +5253257444*a(n-11) +16399879057*a(n-12) -30419637636*a(n-13) -37486637674*a(n-14) +87632998667*a(n-15) +40083109062*a(n-16) -140235056122*a(n-17) -7589163210*a(n-18) +128111780723*a(n-19) -23221600421*a(n-20) -65939015129*a(n-21) +21868944788*a(n-22) +18307048178*a(n-23) -8259596531*a(n-24) -2431120428*a(n-25) +1497147381*a(n-26) +85285300*a(n-27) -123174410*a(n-28) +8581030*a(n-29) +3300116*a(n-30) -512304*a(n-31) +18304*a(n-32)

cp's OEIS Frontend

A208263 Number of n X n 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 left-upward diagonal neighbors.

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A208264 Number of n X 3 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 left-upward diagonal neighbors.

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A208265 Number of n X 4 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 left-upward diagonal neighbors.

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A208266 Number of nX5 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 left-upward diagonal neighbors.

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A208267 Number of nX6 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 left-upward diagonal neighbors.

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A208268 Number of nX7 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 left-upward diagonal neighbors.

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