A183644 Number of (n+1) X 2 0..4 arrays with every 2 X 2 subblock summing to 8.

85, 325, 1333, 5725, 25405, 115525, 535333, 2517805, 11982925, 57575125, 278766133, 1358125885, 6649985245, 32693825125, 161264049733, 797557733965, 3952911584365, 19625567713525, 97573430562133, 485654176126045, 2419432933612285, 12061854746568325, 60168159621439333

Offset

1,1

Links

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

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

Formula

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

Conjectures from Colin Barker, Mar 31 2018: (Start)

G.f.: x*(85 - 950*x + 3683*x^2 - 5770*x^3 + 3000*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)).

a(n) = 2 + 2^(2+n) + 2^(3+2*n) + 2*3^(1+n) + 5^(1+n). (End)

The formulas are correct. The proof is similar to the one in A183654. - Jianing Song, Jun 12 2026

E.g.f.: 5*exp(5*x) + 8*exp(4*x) + 6*exp(3*x) + 4*exp(2*x) + 2*exp(x) - 25. - Stefano Spezia, Jun 18 2026

Example

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

Mathematica

A183644[n_] := 2 + 2^(n+2) + 2^(2*n+3) + 2*3^(n+1) + 5^(n+1);
Array[A183644, 25] (* Paolo Xausa, Jun 18 2026 *)

Crossrefs

Column 1 of A183652.

Cf. A183654.

Sequence in context: A020200 A020298 A183652 * A068559 A045017 A297399

Adjacent sequences: A183641 A183642 A183643 * A183645 A183646 A183647

Keyword

nonn,easy

Author

R. H. Hardin, Jan 06 2011

Status

approved