A183641 Number of (n+1) X 9 0..3 arrays with every 2 X 2 subblock summing to 6.

302536, 386404, 563416, 945364, 1793416, 3743524, 8411896, 20077684, 50494696, 132978244, 364466776, 1033299604, 3013698376, 9003358564, 27471920056, 85487379124, 271195756456, 877414692484, 2897338323736, 9771959724244, 33674792380936, 118538297028004, 425827103389816, 1558643223582964

Offset

1,1

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

Christian Krause, Proof of formula, Jun 23 2026.

Formula

a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4).

a(n) = 4*4^n + 1530*3^n + 37320*2^n + 223290. - Christian Krause, Jun 23 2026

Example

Some solutions for 3 X 9:
  2  0  2  2  0  0  3  0  2    0  2  3  0  3  0  2  2  3
  1  3  1  1  3  3  0  3  1    3  1  0  3  0  3  1  1  0
  2  0  2  2  0  0  3  0  2    0  2  3  0  3  0  2  2  3

Mathematica

A183641[n_] := 4*4^n + 1530*3^n + 37320*2^n + 223290;
Array[A183641, 25] (* Paolo Xausa, Jun 24 2026 *)

Crossrefs

Column 8 of A183642.

Sequence in context: A156998 A156999 A111031 * A212230 A185852 A053849

Adjacent sequences: A183638 A183639 A183640 * A183642 A183643 A183644

Keyword

nonn,easy

Author

R. H. Hardin, Jan 06 2011

Extensions

a(10)-a(24) from Christian Krause, Jun 23 2026

Status

approved