A183656 Number of (n+1) X 4 0..5 arrays with every 2 X 2 subblock summing to 10.

3254, 9990, 35162, 135966, 563114, 2458590, 11196842, 52793406, 256308074, 1275989790, 6492865322, 33682946046, 177764461034, 952702906590, 5176836594602, 28481036093886, 158444359333994, 890260394424990, 5046661814128682, 28833724226476926, 165883366948958954, 960152023010640990

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 (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.: 2*x*(1627 - 29172*x + 197411*x^2 - 622938*x^3 + 901512*x^4 - 466560*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 + 70*5^n + 200*4^n + 330*3^n + 388*2^n + 302. - Christian Krause, Jun 12 2026

Example

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

Mathematica

A183656[n_] := 6*6^n + 70*5^n + 200*4^n + 330*3^n + 388*2^n + 302;
Array[A183656, 25] (* Paolo Xausa, Jun 17 2026 *)

Crossrefs

Column 3 of A183662.

Sequence in context: A031735 A144936 A164077 * A043606 A135134 A137836

Adjacent sequences: A183653 A183654 A183655 * A183657 A183658 A183659

Keyword

nonn,easy,changed

Author

R. H. Hardin, Jan 06 2011

Status

approved