A183639 Number of (n+1) X 7 0..3 arrays with every 2 X 2 subblock summing to 6.

21016, 31060, 53512, 105604, 231736, 551380, 1398952, 3743524, 10479256, 30483700, 91664392, 283832644, 902755576, 2945024020, 9845481832, 33704772964, 118040932696, 422335788340, 1540872323272, 5720102724484, 21554302962616, 82246991512660, 317093511900712, 1232723098807204

Offset

1,1

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000 (terms 1..77 from R. H. Hardin).

Christian Krause, Proof of formula, Jun 23 2026.

Formula

a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4).

From Colin Barker, Mar 31 2018: (Start)

G.f.: 4*x*(5254 - 44775*x + 119618*x^2 - 98304*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)).

a(n) = 12138 + 483*2^(3+n) + 14*3^(3+n) + 4^(1+n).

(End) [proved by Christian Krause, Jun 23 2026]

E.g.f.: 2*(2*exp(4*x) + 189*exp(3*x) + 1932*exp(2*x) + 6069*exp(x) - 8192). - Stefano Spezia, Jun 24 2026

Example

Some solutions for 3 X 7:
  0 0 1 3 1 2 3     3 2 3 3 0 0 1     3 0 1 0 3 1 3
  3 3 2 0 2 1 0     0 1 0 0 3 3 2     1 2 3 2 1 1 1
  0 0 1 3 1 2 3     3 2 3 3 0 0 1     2 1 0 1 2 2 2

Mathematica

A183639[n_] := 12138 + 483*2^(n+3) + 14*3^(n+3) + 4^(n+1);
Array[A183639, 25] (* Paolo Xausa, Jun 24 2026 *)

Crossrefs

Column 6 of A183642.

Sequence in context: A344355 A231314 A157083 * A181260 A316482 A340897

Adjacent sequences: A183636 A183637 A183638 * A183640 A183641 A183642

Keyword

nonn,easy,changed

Author

R. H. Hardin, Jan 06 2011

Status

approved