A183665 Number of (n+1) X 3 0..6 arrays with every 2 X 2 subblock summing to 12.

1225, 5215, 24745, 126223, 678265, 3791935, 21874825, 129463663, 782782105, 4819857055, 30146536105, 191148081103, 1226597365945, 7954555064575, 52068989200585, 343658085034543, 2284795961645785, 15288911173702495, 102893501041260265, 695969029772579983, 4728478913748837625

Offset

1,1

Links

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

Christian Krause, Proof of formulas, Jun 12 2026.

Index entries for linear recurrences with constant coefficients, signature (28,-322,1960,-6769,13132,-13068,5040).

Formula

a(n) = 28*a(n-1) - 322*a(n-2) + 1960*a(n-3) - 6769*a(n-4) + 13132*a(n-5) - 13068*a(n-6) + 5040*a(n-7).

G.f.: x*(1225 - 29085*x + 273175*x^2 - 1288407*x^3 + 3182536*x^4 - 3842244*x^5 + 1728720*x^6) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)). - Colin Barker, Apr 02 2018

a(n) = 7*7^n + 36*6^n + 60*5^n + 72*4^n + 72*3^n + 60*2^n + 36. - Christian Krause, Jun 12 2026

Example

Some solutions for 5 X 3:
..2..6..2....1..3..2....4..3..4....0..4..0....3..3..3....3..2..2....0..6..2
..4..0..4....4..4..3....3..2..3....3..5..3....6..0..6....3..4..4....2..4..0
..6..2..6....2..2..3....3..4..3....3..1..3....1..5..1....5..0..4....2..4..4
..1..3..1....5..3..4....2..3..2....6..2..6....2..4..2....5..2..6....6..0..4
..5..3..5....2..2..3....3..4..3....0..4..0....1..5..1....3..2..2....4..2..6

Mathematica

A183665[n_] := 7*7^n + 36*6^n + 60*5^n + 72*4^n + 72*3^n + 60*2^n + 36;
Array[A183665, 25] (* Paolo Xausa, Jun 15 2026 *)

Crossrefs

Column 2 of A183672.

Sequence in context: A275256 A350323 A350345 * A250848 A014795 A267297

Adjacent sequences: A183662 A183663 A183664 * A183666 A183667 A183668

Keyword

nonn,easy,changed

Author

R. H. Hardin, Jan 06 2011

Status

approved