A183657 Number of (n+1) X 5 0..5 arrays with every 2 X 2 subblock summing to 10.

16626, 43986, 135966, 469146, 1755246, 6990906, 29275086, 127755066, 577190766, 2686295226, 12829230606, 62680963386, 312535936686, 1587207989946, 8196463880526, 42981002402106, 228591556161006, 1231705534203066, 6717082333512846, 37039678928039226, 206331763801191726

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..163

Christian Krause, Proof of formulas, Jun 12 2026.

Index entries for linear recurrences with constant coefficients, signature (21,-175,735,-1624,1764,-720).

Formula

a(n) = 21*a(n-1) - 175*a(n-2) + 735*a(n-3) - 1624*a(n-4) + 1764*a(n-5) - 720*a(n-6).

G.f.: 6*x*(2771 - 50860*x + 353635*x^2 - 1151450*x^3 + 1728024*x^4 - 933120*x^5) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)). - Colin Barker, Apr 02 2018

a(n) = 6*6^n + 150*5^n + 720*4^n + 1710*3^n + 2640*2^n + 2550. - Christian Krause, Jun 12 2026

Example

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

Mathematica

A183657[n_] := 6*6^n + 150*5^n + 720*4^n + 1710*3^n + 2640*2^n + 2550;
Array[A183657, 25] (* Paolo Xausa, Jun 17 2026 *)

Crossrefs

Column 4 of A183662.

Sequence in context: A236638 A250930 A210272 * A247693 A170788 A057329

Adjacent sequences: A183654 A183655 A183656 * A183658 A183659 A183660

Keyword

nonn,easy,changed

Author

R. H. Hardin, Jan 06 2011

Status

approved