A197409 -id:A197409 - cp's OEIS frontend

A197403 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,1,1 for x=0,1,2,3,4.

3, 9, 20, 71, 227, 664, 2107, 6675, 20696, 65029, 205057, 643930, 2026105, 6384135, 20104382, 63329883, 199576691, 628932096, 1982100085, 6247388117, 19691746204, 62069757373, 195654894641, 616749232724, 1944155102539, 6128552692107

Offset: 1

R. H. Hardin, Oct 14 2011

nonn

Every 0 is next to 0 3's, every 1 is next to 1 0'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 A197409.

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

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

Cf. A197409.

Empirical: a(n) = 2*a(n-1) + 4*a(n-2) + 7*a(n-3) - 10*a(n-4) - 39*a(n-5) - 30*a(n-6) - 12*a(n-7) + 5*a(n-8) + 2*a(n-9).

Empirical g.f.: x*(1 + x)^2*(3 - 3*x - 7*x^2 - 9*x^3 - 3*x^4 + 8*x^5 + 2*x^6) / (1 - 2*x - 4*x^2 - 7*x^3 + 10*x^4 + 39*x^5 + 30*x^6 + 12*x^7 - 5*x^8 - 2*x^9). - Colin Barker, Mar 01 2018

A197404 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

4, 20, 60, 358, 1626, 7232, 34717, 160988, 748843, 3514426, 16448990, 76889286, 359867470, 1684122959, 7879951514, 36879246800, 172597946528, 807735845097, 3780221117751, 17691605965676, 82797291928191, 387496301051514

Offset: 1

R. H. Hardin Oct 14 2011

nonn

Every 0 is next to 0 3's, every 1 is next to 1 0'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 3 of A197409

			Some solutions for n=4
..1..0..0....1..0..0....0..0..0....1..0..0....1..0..1....1..1..0....0..0..0
..2..1..1....2..0..0....0..2..1....1..1..2....1..2..1....0..1..1....1..1..1
..0..2..1....1..2..1....2..1..2....0..2..1....0..0..0....0..1..2....2..1..3
..0..0..0....0..0..1....1..0..0....0..0..0....1..1..1....1..2..0....0..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) +8*a(n-3) -37*a(n-4) -13*a(n-5) -58*a(n-6) -814*a(n-7) -2710*a(n-8) -1095*a(n-9) +6385*a(n-10) +15988*a(n-11) +42018*a(n-12) +47855*a(n-13) +32250*a(n-14) -50035*a(n-15) -77306*a(n-16) -41809*a(n-17) -25413*a(n-18) -49387*a(n-19) -14658*a(n-20) +11927*a(n-21) +12328*a(n-22) +6216*a(n-23) +17403*a(n-24) +12464*a(n-25) -363*a(n-26) +6490*a(n-27) -2100*a(n-28) +61*a(n-29) -629*a(n-30) -131*a(n-31) +42*a(n-32) +a(n-33) +a(n-34)

A197405 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

5, 71, 358, 3305, 25621, 199384, 1634731, 13013551, 103260478, 825286477, 6597403489, 52719871616, 421012069157, 3360781198751, 26839340562982, 214392512110323, 1712358386200271, 13675010695945780, 109210026376844947

Offset: 1

R. H. Hardin Oct 14 2011

nonn

Every 0 is next to 0 3's, every 1 is next to 1 0'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 A197409

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

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

A197406 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

9, 227, 1626, 25621, 356211, 4499426, 60334353, 801294395, 10631272297, 141478252511, 1877225887699, 24928405579380, 331380977085358, 4402455983432465, 58475570189400714, 776864156510384965

Offset: 1

R. H. Hardin Oct 14 2011

nonn

Every 0 is next to 0 3's, every 1 is next to 1 0'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 A197409

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

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

A197407 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

16, 664, 7232, 199384, 4499426, 93153650, 2065093081, 45796265386, 1003308210971, 22026879283832, 484764553481336, 10667288376795442, 234488008953014630, 5155498381464737047, 113400638560649259216

Offset: 1

R. H. Hardin Oct 14 2011

nonn

Every 0 is next to 0 3's, every 1 is next to 1 0'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 A197409

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

R. H. Hardin, Table of n, a(n) for n = 1..164

A197408 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

25, 2107, 34717, 1634731, 60334353, 2065093081, 77683473682, 2861267797023, 104224692369107, 3821001855576417, 140295906943370100, 5143358134125047217, 188539285472381998575, 6914680866283564114758, 253564501233044701809946

Offset: 1

R. H. Hardin Oct 14 2011

nonn

Every 0 is next to 0 3's, every 1 is next to 1 0'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 A197409

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

R. H. Hardin, Table of n, a(n) for n = 1..51

A197402 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,0,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

1, 9, 60, 3305, 356211, 93153650, 77683473682, 174585377113223

Offset: 1

R. H. Hardin Oct 14 2011

nonn

Every 0 is next to 0 3's, every 1 is next to 1 0'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 A197409

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

cp's OEIS Frontend

A197403 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,1,1 for x=0,1,2,3,4.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A197404 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,1,1 for x=0,1,2,3,4.

Views

Author

Keywords

Comments

Examples

Links

Formula

A197405 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,1,1 for x=0,1,2,3,4.

Views

Author

Keywords

Comments

Examples

Links

A197406 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,1,1 for x=0,1,2,3,4.

Views

Author

Keywords

Comments

Examples

Links

A197407 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,1,1 for x=0,1,2,3,4.

Views

Author

Keywords

Comments

Examples

Links

A197408 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,1,1 for x=0,1,2,3,4.

Views

Author

Keywords

Comments

Examples

Links

A197402 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,0,1,1,1 for x=0,1,2,3,4.

Views

Author

Keywords

Comments

Examples