A197672 -id:A197672 - cp's OEIS frontend

A197666 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,0,1 for x=0,1,2,3,4.

3, 9, 22, 71, 217, 642, 1963, 5963, 18018, 54753, 166329, 504940, 1534985, 4667983, 14198968, 43215503, 131584139, 400800484, 1221337807, 3723140135, 11353757744, 34635822651, 105696236527, 322652635812, 985253141189, 3009481166143

Offset: 1

R. H. Hardin, Oct 17 2011

nonn

Every 0 is next to 0 4's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 1's.

Column 2 of A197672.

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

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A197672.

Empirical: a(n) = 3*a(n-1) +4*a(n-2) -25*a(n-4) -37*a(n-5) +4*a(n-6) +23*a(n-7) +17*a(n-8) -5*a(n-9) -a(n-10).

Empirical g.f.: x*(1 - x)*(1 + x)^2*(3 - 3*x - 11*x^2 - 20*x^3 - 3*x^4 + 15*x^5 + 2*x^6) / ((1 - x - 5*x^2 - 4*x^3 - x^4 + x^5)*(1 - 2*x - x^2 - 7*x^3 + 6*x^4 + x^5)). - Colin Barker, May 14 2018

A197667 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,0,1 for x=0,1,2,3,4.

Original entry on oeis.org

4, 22, 95, 546, 2765, 14503, 74812, 386556, 2008698, 10415923, 54096117, 280793815, 1457402796, 7564115674, 39256668738, 203743660496, 1057439556784, 5488205547156, 28484308704921, 147836021658293, 767281388051654

Offset: 1

R. H. Hardin, Oct 17 2011

nonn

Every 0 is next to 0 4's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 1's.

Column 3 of A197672.

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

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A197672.

Empirical: a(n) = 5*a(n-1) +7*a(n-2) -24*a(n-3) -44*a(n-4) +67*a(n-5) +50*a(n-6) -412*a(n-7) -2205*a(n-8) -7418*a(n-9) -6654*a(n-10) -2331*a(n-11) +42455*a(n-12) +97689*a(n-13) +188061*a(n-14) +169272*a(n-15) -162775*a(n-16) -268709*a(n-17) -801522*a(n-18) -429147*a(n-19) +162997*a(n-20) -228546*a(n-21) +1079921*a(n-22) +1138660*a(n-23) +160033*a(n-24) -1361447*a(n-25) -51481*a(n-26) +285711*a(n-27) +152964*a(n-28) -624541*a(n-29) +374389*a(n-30) +62069*a(n-31) -30580*a(n-32) +83333*a(n-33) -134862*a(n-34) +17843*a(n-35) +16897*a(n-36) +7673*a(n-37) -3585*a(n-38) -1901*a(n-39) +2034*a(n-40) -729*a(n-41) +137*a(n-42) -105*a(n-43).

A197668 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,0,1 for x=0,1,2,3,4.

Original entry on oeis.org

5, 71, 546, 5005, 44323, 403960, 3675345, 33272751, 301565202, 2734015025, 24796812073, 224875172500, 2039110071283, 18490725428895, 167679905896100, 1520586052304877, 13789181642921163, 125044668702632018

Offset: 1

R. H. Hardin Oct 17 2011

nonn

Every 0 is next to 0 4's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 1's

Column 4 of A197672

			Some solutions containing all values 0 to 4 for n=5
..0..0..0..1....0..2..1..0....1..0..1..2....0..2..1..0....0..1..1..0
..0..3..0..1....0..1..4..1....2..1..4..1....0..1..4..1....1..4..1..2
..1..1..0..1....0..2..1..2....0..2..1..0....2..1..1..1....2..1..0..1
..1..4..1..2....3..0..0..0....3..0..2..0....1..0..0..0....0..3..0..1
..0..1..1..0....0..3..0..0....0..0..1..1....1..0..3..0....0..0..0..1

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

A197669 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,0,1 for x=0,1,2,3,4.

Original entry on oeis.org

9, 217, 2765, 44323, 709083, 11277331, 178113620, 2824369075, 44803424135, 710299706355, 11259206241825, 178502455899971, 2830080961456550, 44867619862024252, 711321096455186766, 11277240691421407939

Offset: 1

R. H. Hardin Oct 17 2011

nonn

Every 0 is next to 0 4's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 1's

Column 5 of A197672

			Some solutions containing all values 0 to 4 for n=4
..0..1..2..0..0....0..0..0..1..2....0..0..2..1..0....0..2..1..1..1
..0..1..1..0..3....0..3..1..4..1....3..0..1..4..1....1..1..0..0..0
..1..4..1..2..0....3..0..1..1..0....0..0..1..1..2....1..4..1..3..0
..2..1..0..1..1....0..0..2..1..0....1..2..1..0..0....0..1..1..0..0

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

A197670 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,0,1 for x=0,1,2,3,4.

Original entry on oeis.org

16, 642, 14503, 403960, 11277331, 311676959, 8613257822, 239118653300, 6630227642552, 183756345226485, 5094599088185193, 141246701196281961, 3915786139554013344, 108558677747367102730, 3009656266880644396542

Offset: 1

R. H. Hardin Oct 17 2011

nonn

Every 0 is next to 0 4's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 1's

Column 6 of A197672

			Some solutions containing all values 0 to 4 for n=4
..0..0..1..1..0..0....0..3..0..0..0..0....1..1..0..1..1..0....0..0..2..1..0..0
..1..1..4..1..0..3....3..0..3..2..1..1....0..2..1..4..1..2....0..0..1..4..1..1
..2..1..1..1..0..0....0..0..0..1..4..1....3..0..1..1..0..1....0..0..2..1..1..1
..0..0..0..1..1..1....0..3..0..2..1..0....0..0..1..1..0..1....0..3..0..0..0..0

R. H. Hardin, Table of n, a(n) for n = 1..133

A197671 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,0,1 for x=0,1,2,3,4.

Original entry on oeis.org

25, 1963, 74812, 3675345, 178113620, 8613257822, 417293944115, 20252638815131, 981414876628367, 47569549221404522, 2306162325188337684, 111794015697526614448, 5419263655984491978357, 262704965350074163519109

Offset: 1

R. H. Hardin Oct 17 2011

nonn

Every 0 is next to 0 4's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 1's

Column 7 of A197672

			Some solutions containing all values 0 to 4 for n=4
..0..3..0..2..1..0..1....0..0..2..1..1..1..1....0..3..0..2..1..0..0
..0..0..0..1..4..1..1....1..1..1..0..0..0..0....3..0..0..1..4..1..1
..0..3..0..2..1..1..0....1..1..4..1..3..0..3....0..3..0..1..1..1..2
..1..1..0..0..0..2..1....0..0..1..1..0..0..0....1..2..1..1..0..0..0

R. H. Hardin, Table of n, a(n) for n = 1..33

A197665 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,0,1,0,1 for x=0,1,2,3,4.

Original entry on oeis.org

1, 9, 95, 5005, 709083, 311676959, 417293944115, 1717065757366333

Offset: 1

R. H. Hardin Oct 17 2011

nonn

Every 0 is next to 0 4's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 1's

Diagonal of A197672

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

cp's OEIS Frontend

A197666 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,0,1 for x=0,1,2,3,4.

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A197667 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,0,1 for x=0,1,2,3,4.

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A197668 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,0,1 for x=0,1,2,3,4.

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A197669 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,0,1 for x=0,1,2,3,4.

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A197670 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,0,1 for x=0,1,2,3,4.

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A197671 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,0,1 for x=0,1,2,3,4.

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A197665 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,0,1,0,1 for x=0,1,2,3,4.

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