A208864 -id:A208864 - cp's OEIS frontend

A208858 Number of n X 2 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or left-upward diagonal neighbors.

2, 11, 127, 1691, 23047, 315203, 4313071, 59022155, 807696535, 11053048211, 151257183487, 2069902880411, 28325913895207, 387630456564323, 5304590398318351, 72591507756551915, 993389989178417335

Offset: 1

R. H. Hardin, Mar 02 2012

nonn

Column 2 of A208864.

			Some solutions for n=4:
..0..0....0..0....0..0....0..0....0..1....0..0....0..0....0..0....0..0....0..1
..0..1....0..1....1..1....1..1....1..0....0..1....0..1....1..1....0..1....1..2
..0..2....1..0....0..2....2..0....0..1....0..1....1..2....0..0....1..0....3..3
..1..3....1..2....2..0....1..2....0..1....0..2....2..0....0..1....2..2....3..1

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

Cf. A208864.

Empirical: a(n) = 17*a(n-1) - 48*a(n-2) + 36*a(n-3) for n>4.

Empirical g.f.: x*(2 - 23*x + 36*x^2 - 12*x^3) / ((1 - 2*x)*(1 - 15*x + 18*x^2)). - Colin Barker, Jul 07 2018

A208859 Number of n X 3 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or left-upward diagonal neighbors.

Original entry on oeis.org

5, 127, 5796, 273049, 12883280, 607924387, 28686344276, 1353633375649, 63874412830520, 3014066220322507, 142225889552418956, 6711267165754821049, 316687117317930292160, 14943635501046735026227, 705151014286332805949636

Offset: 1

R. H. Hardin, Mar 02 2012

nonn

Column 3 of A208864.

			Some solutions for n=4:
..0..1..1....0..1..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
..0..1..0....0..2..2....0..1..1....0..1..1....0..1..1....0..1..1....1..1..1
..0..1..2....1..2..1....0..1..2....2..1..2....1..2..0....2..1..2....0..2..0
..3..2..1....1..3..2....2..0..2....0..2..1....1..0..1....2..1..2....0..1..0

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

Cf. A208864.

Empirical: a(n) = 59*a(n-1) - 603*a(n-2) + 2211*a(n-3) - 2826*a(n-4) + 720*a(n-5) for n>6.

Empirical g.f.: x*(5 - 168*x + 1318*x^2 - 3389*x^3 + 1710*x^4 - 240*x^5) / ((1 - 2*x)*(1 - 57*x + 489*x^2 - 1233*x^3 + 360*x^4)). - Colin Barker, Jul 07 2018

A208860 Number of nX4 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or left-upward diagonal neighbors.

Original entry on oeis.org

15, 1691, 273049, 44452082, 7240366702, 1179377179523, 192108983085145, 31292693945057258, 5097277404701734234, 830297232890575975631, 135247396001465780031025, 22030493903508619572329906

Offset: 1

R. H. Hardin Mar 02 2012

nonn

Column 4 of A208864

			Some solutions for n=4
..0..0..1..0....0..0..1..2....0..0..0..0....0..1..1..0....0..0..0..1
..0..2..2..0....0..3..3..0....1..1..1..1....0..1..2..0....1..1..1..2
..2..3..3..0....1..0..1..2....2..2..2..3....0..2..1..1....2..2..2..0
..1..2..0..2....1..2..0..0....0..1..3..0....3..1..0..0....0..3..0..1

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

Empirical: a(n) = 219*a(n-1) -10289*a(n-2) +197167*a(n-3) -1651023*a(n-4) +4615685*a(n-5) +5157645*a(n-6) -45444123*a(n-7) +78064236*a(n-8) -63363708*a(n-9) +40081392*a(n-10) -18662400*a(n-11) for n>12

A208861 Number of nX5 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or left-upward diagonal neighbors.

Original entry on oeis.org

51, 23047, 12883280, 7240366702, 4071491223248, 2289701830963879, 1287681340443915644, 724166398812363542260, 407256849342915985761092, 229033195050822330468202369, 128803738036903910358389563556

Offset: 1

R. H. Hardin Mar 02 2012

nonn

Column 5 of A208864

			Some solutions for n=4
..0..0..0..0..1....0..0..0..0..0....0..1..0..0..0....0..1..1..0..0
..1..1..1..2..1....0..1..1..2..2....1..0..1..1..1....0..1..2..0..1
..2..3..0..1..2....2..2..3..2..3....1..0..2..3..2....3..2..3..1..2
..0..0..1..3..0....3..1..1..2..1....3..2..3..1..1....2..0..1..0..0

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

Empirical: a(n) = 831*a(n-1) -179993*a(n-2) +17822337*a(n-3) -914949819*a(n-4) +23168761555*a(n-5) -161356715633*a(n-6) -4487021565447*a(n-7) +88170625092243*a(n-8) -89146256087223*a(n-9) -9123849468343275*a(n-10) +57411954474413179*a(n-11) +280936943350232287*a(n-12) -3595338835588287543*a(n-13) +1929659835323795485*a(n-14) +90093226296032329771*a(n-15) -288134852946702870262*a(n-16) -742914836218346528932*a(n-17) +7115855576376274368216*a(n-18) -24955774603971431557536*a(n-19) +63937383750208880620992*a(n-20) -111375370598187857506560*a(n-21) +72057203548966403859456*a(n-22) +76274285418217337610240*a(n-23) -111975434876548575756288*a(n-24) +5300659781619687751680*a(n-25) +29374280040899283517440*a(n-26) -7836898836947747733504*a(n-27) for n>28

A208862 Number of nX6 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or left-upward diagonal neighbors.

Original entry on oeis.org

187, 315203, 607924387, 1179377179523, 2289701830963879, 4445765748006060562, 8632160191264007914496, 16760735467624113550972052, 32543685580973709708760951442, 63188843847651604770766546682829

Offset: 1

R. H. Hardin Mar 02 2012

nonn

Column 6 of A208864

			Some solutions for n=4
..0..1..0..0..2..2....0..0..0..0..0..1....0..0..0..0..0..0....0..0..0..0..0..0
..1..2..1..1..3..3....0..1..2..1..3..2....0..1..1..1..2..1....1..2..1..1..1..3
..0..3..3..0..1..0....1..3..0..3..1..0....0..1..0..2..3..1....1..3..3..2..2..3
..2..1..1..2..1..2....2..1..0..3..0..3....0..3..1..0..1..0....0..1..0..0..1..0

R. H. Hardin, Table of n, a(n) for n = 1..136

A208863 Number of nX7 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or left-upward diagonal neighbors.

Original entry on oeis.org

715, 4313071, 28686344276, 192108983085145, 1287681340443915644, 8632160191264007914496, 57867813487534623493632032, 387931894337100662003223085624, 2600602689186684798782025006594196

Offset: 1

R. H. Hardin Mar 02 2012

nonn

Column 7 of A208864

			Some solutions for n=4
..0..0..1..2..1..1..3....0..1..2..3..0..1..2....0..0..0..0..0..0..1
..2..1..3..3..0..2..3....0..1..2..3..0..2..0....1..1..1..1..1..1..0
..2..1..2..2..1..1..0....3..0..2..0..3..1..1....2..3..2..2..2..0..3
..2..0..3..0..0..2..1....2..0..2..0..1..0..3....3..0..1..0..0..3..2

R. H. Hardin, Table of n, a(n) for n = 1..42

A208857 Number of n X n 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or left-upward diagonal neighbors.

Original entry on oeis.org

1, 11, 5796, 44452082, 4071491223248, 4445765748006060562, 57867813487534623493632032, 8978812485595759770697498996138448

Offset: 1

R. H. Hardin Mar 02 2012

nonn

Diagonal of A208864

			Some solutions for n=4
..0..1..0..0....0..0..1..0....0..0..0..1....0..0..0..1....0..1..1..2
..2..2..1..2....2..1..2..2....1..1..1..2....0..1..1..0....0..1..0..0
..1..1..3..2....1..3..0..0....2..2..2..0....0..1..2..3....0..1..3..1
..0..3..0..0....1..3..2..2....0..3..0..1....3..0..3..1....1..2..2..0

cp's OEIS Frontend

A208858 Number of n X 2 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or left-upward diagonal neighbors.

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A208859 Number of n X 3 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or left-upward diagonal neighbors.

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A208860 Number of nX4 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or left-upward diagonal neighbors.

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A208861 Number of nX5 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or left-upward diagonal neighbors.

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A208862 Number of nX6 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or left-upward diagonal neighbors.

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A208863 Number of nX7 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or left-upward diagonal neighbors.

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A208857 Number of n X n 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or left-upward diagonal neighbors.

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