A183666 Number of (n+1) X 4 0..6 arrays with every 2 X 2 subblock summing to 12.

6951, 24745, 100935, 451801, 2163831, 10914505, 57370215, 311907001, 1744391511, 9994250665, 58473101895, 348467631001, 2110957895991, 12976935385225, 80838681063975, 509665597255801, 3248622235733271, 20914068068750185, 135868479072424455, 889990846016813401, 5873675421582639351

Offset

1,1

Links

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

Christian Krause, Proof of formulas, Jun 12 2026.

Index entries for linear recurrences with constant coefficients, signature (28,-322,1960,-6769,13132,-13068,5040).

Formula

a(n) = 28*a(n-1) - 322*a(n-2) + 1960*a(n-3) - 6769*a(n-4) + 13132*a(n-5) - 13068*a(n-6) + 5040*a(n-7).

G.f.: x*(6951 - 169883*x + 1646297*x^2 - 8030449*x^3 + 20565592*x^4 - 25807068*x^5 + 12101040*x^6) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)). - Colin Barker, Apr 02 2018

a(n) = 7*7^n + 84*6^n + 250*5^n + 440*4^n + 582*3^n + 604*2^n + 434. - Christian Krause, Jun 12 2026

Example

Some solutions for 3 X 4:
..0..6..2..2....1..4..1..5....6..5..3..3....4..1..5..0....5..4..3..3
..5..1..3..5....1..6..1..5....1..0..4..2....6..1..5..2....1..2..3..3
..1..5..3..1....1..4..1..5....6..5..3..3....1..4..2..3....3..6..1..5

Mathematica

A183666[n_] := 7*7^n + 84*6^n + 250*5^n + 440*4^n + 582*3^n + 604*2^n + 434;
Array[A183666, 25] (* Paolo Xausa, Jun 15 2026 *)

Crossrefs

Column 3 of A183672.

Sequence in context: A195280 A059462 A252432 * A252368 A237468 A028542

Adjacent sequences: A183663 A183664 A183665 * A183667 A183668 A183669

Keyword

nonn,easy,changed

Author

R. H. Hardin, Jan 06 2011

Status

approved