A183647 Number of (n+1) X 5 0..4 arrays with every 2 X 2 subblock summing to 8.

5725, 12785, 33325, 97145, 307525, 1037585, 3684925, 13653545, 52436725, 207712385, 845452525, 3525617945, 15026853925, 65331315185, 289222676125, 1301655470345, 5946166679125, 27529329445985, 128980999355725, 610662612490745, 2917602353832325, 14048941834104785, 68099740956291325

Offset

1,1

Links

Zhuorui He, Table of n, a(n) for n = 1..1000 (first 200 terms from R. H. Hardin)

Christian Krause, Proof of formulas, Jun 12 2026.

Index entries for linear recurrences with constant coefficients, signature (15,-85,225,-274,120).

Formula

a(n) = 15*a(n-1) - 85*a(n-2) + 225*a(n-3) - 274*a(n-4) + 120*a(n-5).

G.f.: 5*x*(1145 - 14618*x + 65635*x^2 - 120826*x^3 + 75000*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)). - Colin Barker, Apr 01 2018

a(n) = 5*5^n + 120*4^n + 540*3^n + 1140*2^n + 1320. - Christian Krause, Jun 12 2026

E.g.f.: 5*(exp(5*x) + 24*exp(4*x) + 108*exp(3*x) + 228*exp(2*x) + 264*exp(x) - 625). - Stefano Spezia, Jun 17 2026

Example

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

Mathematica

A183647[n_] := 5*5^n + 120*4^n + 540*3^n + 1140*2^n + 1320;
Array[A183647, 25] (* Paolo Xausa, Jun 17 2026 *)

Crossrefs

Column 4 of A183652.

Cf. A183643-A183651.

Sequence in context: A202376 A330208 A252422 * A028547 A224726 A378491

Adjacent sequences: A183644 A183645 A183646 * A183648 A183649 A183650

Keyword

nonn,easy

Author

R. H. Hardin, Jan 06 2011

Status

approved