A197889 -id:A197889 - cp's OEIS frontend

A197883 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,1,1 for x=0,1,2,3,4.

0, 4, 3, 14, 18, 43, 78, 154, 305, 572, 1178, 2185, 4440, 8408, 16795, 32212, 63608, 123295, 241494, 470486, 918795, 1793434, 3497978, 6831997, 13324168, 26019470, 50755921, 99095168, 193344576, 377408195, 736481712, 1437442548, 2805273219

Offset: 1

R. H. Hardin, Oct 19 2011

nonn

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

Column 2 of A197889.

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

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

Cf. A197889.

Empirical: a(n) = 3*a(n-2) +2*a(n-3) +a(n-4) -3*a(n-5) -4*a(n-6) +7*a(n-7) -5*a(n-9).

Empirical g.f.: x^2*(4 + 3*x + 2*x^2 + x^3 - 9*x^4 + 5*x^5 - 7*x^7) / ((1 - x)*(1 + x - 2*x^2 - 4*x^3 - 5*x^4 - 2*x^5 + 2*x^6 - 5*x^7 - 5*x^8)). - Colin Barker, May 14 2018

A197884 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

1, 3, 6, 47, 77, 196, 529, 1637, 4235, 11211, 30271, 83254, 225148, 606579, 1638498, 4440639, 12016918, 32485381, 87846790, 237662631, 642926239, 1738933011, 4703362637, 12722244082, 34413103568, 93083202626, 251777401480

Offset: 1

R. H. Hardin, Oct 19 2011

nonn

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

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

R. H. Hardin, Table of n, a(n) for n = 1..200
Robert Israel, Maple-assisted proof of formula

Column 3 of A197889.

Empirical: a(n) = a(n-1) +a(n-2) +4*a(n-3) +12*a(n-4) +7*a(n-5) +21*a(n-6) -22*a(n-7) -6*a(n-8) -64*a(n-9) -136*a(n-10) +16*a(n-11) +112*a(n-12) +621*a(n-13) +473*a(n-14) +396*a(n-15) -294*a(n-16) -1044*a(n-17) -744*a(n-18) -475*a(n-19) +1462*a(n-20) +156*a(n-21) -1601*a(n-22) -627*a(n-23) -2504*a(n-24) -1566*a(n-25) +468*a(n-26) -518*a(n-27) +384*a(n-28) +444*a(n-29) +208*a(n-30) +400*a(n-31) +96*a(n-32).

Empirical formula verified: see link. - Robert Israel, Aug 24 2018

A197885 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

2, 14, 47, 155, 835, 2263, 10827, 38938, 157178, 654028, 2607334, 10482745, 41930639, 169374587, 686689100, 2793219587, 11244612740, 45359859580, 183328706973, 742423862981, 3008747408411, 12158966386525, 49114866456717

Offset: 1

R. H. Hardin Oct 19 2011

nonn

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

Column 4 of A197889

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

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

A197886 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

1, 18, 77, 835, 2730, 17890, 92843, 567991, 3000116, 17111462, 94740977, 537643352, 2995145891, 16728999681, 93489922434, 524952952537, 2940191924830, 16425787144594, 91861015115420, 514650900540840, 2882700958009902

Offset: 1

R. H. Hardin Oct 19 2011

nonn

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

Column 5 of A197889

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

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

A197887 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

1, 43, 196, 2263, 17890, 129294, 1134527, 9389938, 74334188, 612587633, 4957017898, 40458420396, 328259829544, 2682720603080, 21878875862100, 178129467799644, 1450139820586951, 11818051611475707, 96281373184386270

Offset: 1

R. H. Hardin Oct 19 2011

nonn

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

Column 6 of A197889

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

R. H. Hardin, Table of n, a(n) for n = 1..184

A197888 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

3, 78, 529, 10827, 92843, 1134527, 13253562, 145351090, 1728849664, 19259087568, 227927217325, 2573394846501, 29961925871053, 341720932452731, 3939440439598059, 45203853693284547, 520558824415292051

Offset: 1

R. H. Hardin Oct 19 2011

nonn

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

Column 7 of A197889

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

R. H. Hardin, Table of n, a(n) for n = 1..63

A197882 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 0,2,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

1, 4, 6, 155, 2730, 129294, 13253562, 2512321052

Offset: 1

R. H. Hardin Oct 19 2011

nonn

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

Diagonal of A197889

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

cp's OEIS Frontend

A197883 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,1,1 for x=0,1,2,3,4.

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A197884 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,1,1 for x=0,1,2,3,4.

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A197885 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,1,1 for x=0,1,2,3,4.

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A197886 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,1,1 for x=0,1,2,3,4.

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A197887 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,1,1 for x=0,1,2,3,4.

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A197888 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,1,1 for x=0,1,2,3,4.

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A197882 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 0,2,1,1,1 for x=0,1,2,3,4.

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