A199250 Number of nX2 0..3 arrays with values 0..3 introduced in row major order, the number of instances of each value within one of each other, and no element equal to any horizontal or vertical neighbor.

1, 1, 14, 21, 424, 571, 14160, 18157, 508802, 635901, 19257756, 23709063, 756845422, 922808863, 30595342532, 37055004573, 1264116241990, 1523501274001, 53146116905514, 63810625823521, 2266270709962148, 2712945090726795

Offset

1,3

Comments

Column 2 of A199256.

Links

Manuel Kauers and Christoph Koutschan, Table of n, a(n) for n = 1..1000 (terms 1..56 from R. H. Hardin).

M. Kauers and C. Koutschan, Some D-finite and some possibly D-finite sequences in the OEIS, arXiv:2303.02793 [cs.SC], 2023.

Formula

From Manuel Kauers and Christoph Koutschan, Mar 01 2023: (Start)

a(2*n) = coefficient of x^n*y^n*z^n*t^(2*n) in t*x*y*(1 + t*z)/(2*(1 - t*(x + y + z + x*y + x*z + y*z) - 7*t^2*x*y*z)).

a(2*n+1) = coefficient of x^(n+1)*y^(n+1)*z^(n+1)*t^(2*n+1) in t*x*y*(1 + t*z)*(x + y + z + x*y + x*z + y*z)/(2*(1 - t*(x + y + z + x*y + x*z + y*z) - 7*t^2*x*y*z)) for n>0.

Recurrence of order 4 and degree 8 for even indices: (4 + n)^3*(3 + 2*n)*(-13 + 67*n + 529*n^2 + 440*n^3 + 96*n^4)*a(2*n + 8) - 2*(-47232 + 243564*n + 2728691*n^2 + 5650345*n^3 + 5266809*n^4 + 2637037*n^5 + 736180*n^6 + 108160*n^7 + 6528*n^8)*a(2*n + 6) + 2*(-151008 + 3194000*n + 25261108*n^2 + 53468052*n^3 + 53319121*n^4 + 29037852*n^5 + 8890558*n^6 + 1438672*n^7 + 95808*n^8)*a(2*n + 4) - 98*(23232 + 227996*n + 960783*n^2 + 1960439*n^3 + 2151893*n^4 + 1338307*n^5 + 470452*n^6 + 86848*n^7 + 6528*n^8)*a(2*n + 2) + 2401*n^3*(5 + 2*n)*(1119 + 2829*n + 2425*n^2 + 824*n^3 + 96*n^4)*a(2*n) = 0.

Recurrence of order 4 and degree 10 for odd indices: (5 + n)^3*(3 + 2*n)*(-736 + 2812*n + 35991*n^2 + 63072*n^3 + 38589*n^4 + 9720*n^5 + 864*n^6)*a(2*n + 9) - (3 + 2*n)*(-5010656 + 16627420*n + 251763403*n^2 + 561479353*n^3 + 541644308*n^4 + 281844117*n^5 + 85376223*n^6 + 15113172*n^7 + 1453248*n^8 + 58752*n^9)*a(2*n + 7) + (-156900576 + 635576668*n + 9349986451*n^2 + 24663169255*n^3 + 30687106706*n^4 + 21910345387*n^5 + 9644646333*n^6 + 2664337824*n^7 + 450289356*n^8 + 42566688*n^9 + 1724544*n^10)*a(2*n + 5) - 49*(7 + 2*n)*(1228128 + 12549268*n + 55318177*n^2 + 118911819*n^3 + 139678988*n^4 + 95529783*n^5 + 38777853*n^6 + 9129108*n^7 + 1143936*n^8 + 58752*n^9)*a(2*n + 3) + 2401*n^3*(7 + 2*n)*(150312 + 472150*n + 566901*n^2 + 331908*n^3 + 100149*n^4 + 14904*n^5 + 864*n^6)*a(2*n + 1) = 0. (End)

Example

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

Crossrefs

Sequence in context: A266651 A351689 A166628 * A199195 A291618 A266214

Adjacent sequences: A199247 A199248 A199249 * A199251 A199252 A199253

Keyword

nonn

Author

R. H. Hardin, Nov 04 2011

Status

approved