A196685 -id:A196685 - cp's OEIS frontend

A196680 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,2,3 for x=0,1,2,3,4.

4, 20, 58, 292, 1235, 5186, 22461, 96256, 413032, 1780597, 7673860, 33017186, 142219489, 612618957, 2638803566, 11367909928, 48973948677, 210982341958, 908945163931, 3915948771137, 16870934284560, 72684969189462

Offset: 1

R. H. Hardin Oct 05 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 2's, every 4 is next to 4 3's

Column 3 of A196685

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

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

Empirical: a(n) = 4*a(n-1) +4*a(n-2) -6*a(n-3) +10*a(n-4) -60*a(n-5) -160*a(n-6) -634*a(n-7) -1583*a(n-8) +297*a(n-9) +2182*a(n-10) +9602*a(n-11) +42284*a(n-12) +39581*a(n-13) +18230*a(n-14) +15645*a(n-15) -60179*a(n-16) -28875*a(n-17) +1218*a(n-18) -23566*a(n-19) +46466*a(n-20) -35766*a(n-21) -50232*a(n-22) -41220*a(n-23) -33792*a(n-24) +26772*a(n-25) +17644*a(n-26) +18228*a(n-27) +6120*a(n-28) +4281*a(n-29) +3612*a(n-30) +772*a(n-31) -1467*a(n-32) -815*a(n-33) -304*a(n-34) -271*a(n-35) -35*a(n-36) +19*a(n-37) +3*a(n-38)

A196681 Number of n X 4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,2,3 for x=0,1,2,3,4.

Original entry on oeis.org

5, 61, 292, 2245, 15395, 109528, 796557, 5702355, 40479328, 289195575, 2074543871, 14876511544, 106491873717, 761738952927, 5453371319038, 39065425553179, 279802106777205, 2003379491308618, 14343725864416775, 102713433223681069

Offset: 1

R. H. Hardin Oct 05 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 2's, every 4 is next to 4 3's.

Column 4 of A196685.

			Some solutions for n=5
..0..2..1..2....1..0..0..1....1..1..0..0....0..0..1..2....0..0..1..1
..1..1..0..1....1..0..0..1....0..1..2..0....0..0..1..1....1..1..1..0
..2..2..0..1....2..0..2..1....1..1..1..1....1..1..2..0....1..1..1..2
..1..1..0..1....1..2..1..0....1..0..0..1....2..1..0..0....0..0..0..1
..0..2..1..2....0..0..1..1....2..1..1..2....0..2..1..1....1..1..1..2

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

Cf. A196685.

A196682 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,2,3 for x=0,1,2,3,4.

Original entry on oeis.org

9, 189, 1235, 15395, 188078, 2169685, 25142624, 291420839, 3417608122, 40048090008, 466852430720, 5449232674091, 63760228123954, 745737298355388, 8713522565183852, 101832009256003145, 1190660595164563844

Offset: 1

R. H. Hardin Oct 05 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 2's, every 4 is next to 4 3's

Column 5 of A196685

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

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

A196683 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,2,3 for x=0,1,2,3,4.

Original entry on oeis.org

16, 544, 5186, 109528, 2169685, 39696088, 741925729, 14189246566, 269528695666, 5096101360077, 96554573632988, 1834601649407584, 34805324258849319, 659906675083272359, 12522345994463073108, 237662773521226652080

Offset: 1

R. H. Hardin Oct 05 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 2's, every 4 is next to 4 3's

Column 6 of A196685

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

R. H. Hardin, Table of n, a(n) for n = 1..142

A196684 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,2,3 for x=0,1,2,3,4.

Original entry on oeis.org

25, 1629, 22461, 796557, 25142624, 741925729, 23029545105, 718199634805, 22138818455076, 682005890331480, 21125269566890884, 654095412346594187, 20229325302713363751, 625878086264793074895, 19368465617464223064077

Offset: 1

R. H. Hardin Oct 05 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 2's, every 4 is next to 4 3's

Column 7 of A196685

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

R. H. Hardin, Table of n, a(n) for n = 1..32

A196679 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,0,1,2,3 for x=0,1,2,3,4.

Original entry on oeis.org

1, 9, 58, 2245, 188078, 39696088, 23029545105, 36239510088523

Offset: 1

R. H. Hardin Oct 05 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 2's, every 4 is next to 4 3's

Diagonal of A196685

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

cp's OEIS Frontend

A196680 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,2,3 for x=0,1,2,3,4.

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A196681 Number of n X 4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,2,3 for x=0,1,2,3,4.

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A196682 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,2,3 for x=0,1,2,3,4.

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A196683 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,2,3 for x=0,1,2,3,4.

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A196684 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,2,3 for x=0,1,2,3,4.

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A196679 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,0,1,2,3 for x=0,1,2,3,4.

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