A183633 Number of (n+1) X (n+1) 0..3 arrays with every 2 X 2 subblock summing to 6.

44, 340, 2300, 14644, 90524, 551380, 3333500, 20077684, 120698204, 724889620, 4351447100, 26115027124, 156709229084, 940312639060, 5642047759100, 33852802590964, 203118364179164, 1218714832023700, 7312302935085500, 43873859443537204, 263243282168684444, 1579460069551267540

Offset

1,1

Links

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

Christian Krause, Proof of formula, Jun 19 2026

Index entries for linear recurrences with constant coefficients, signature (11,-36,36).

Formula

a(n) = 4*(2^n-1)*3^(n+1)+4*2^n = 12*6^n-12*3^n+4*2^n. - Zhuorui He, Jun 13 2026

From Stefano Spezia, Jun 21 2026: (Start)

G.f.: 4*x*(11 - 36*x + 36*x^2)/((1 - 2*x)*(1 - 3*x)*(1 - 6*x)).

E.g.f.: 4*(3*exp(6*x) - 3*exp(3*x) + exp(2*x) - 1). (End)

Example

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

Mathematica

A183633[n_] := 12*6^n - 12*3^n + 4*2^n;
Array[A183633, 25] (* Paolo Xausa, Jun 22 2026 *)

Crossrefs

Main diagonal of A183642.

Cf. A183634-A183641.

Sequence in context: A001689 A306937 A199828 * A200450 A024304 A190420

Adjacent sequences: A183630 A183631 A183632 * A183634 A183635 A183636

Keyword

nonn,easy,changed

Author

R. H. Hardin, Jan 06 2011

Extensions

a(9)-a(10) from Zhuorui He, Jun 13 2026

a(11)-a(22) from Christian Krause, Jun 19 2026

Status

approved