A183675 Number of (n+1) X 3 0..7 arrays with every 2 X 2 subblock summing to 14.

2080, 10088, 54496, 316232, 1931680, 12267368, 80331616, 539328392, 3696942880, 25792417448, 182701863136, 1311449598152, 9524204728480, 69887478820328, 517576834025056, 3864851916885512, 29073925027240480, 220170830778612008, 1677292110363153376, 12846579564889030472

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 (36,-546,4536,-22449,67284,-118124,109584,-40320).

Formula

a(n) = 36*a(n-1) - 546*a(n-2) + 4536*a(n-3) - 22449*a(n-4) + 67284*a(n-5) - 118124*a(n-6) + 109584*a(n-7) - 40320*a(n-8).

G.f.: 8*x*(260 - 8099*x + 103376*x^2 - 696557*x^3 + 2654612*x^4 - 5661188*x^5 + 6161616*x^6 - 2580480*x^7) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)*(1 - 8*x)). - Colin Barker, Apr 03 2018

a(n) = 8*8^n + 42*7^n + 72*6^n + 90*5^n + 96*4^n + 90*3^n + 72*2^n + 42. - Christian Krause, Jun 12 2026

E.g.f.: 2*(4*exp(8*x) + 21*exp(7*x) + 36*exp(6*x) + 45*exp(5*x) + 48*exp(4*x) + 45*exp(3*x) + 36*exp(2*x) + 21*exp(x) - 256). - Stefano Spezia, Jun 18 2026

Example

Some solutions for 5 X 3:
..6..0..7....0..6..0....6..0..3....6..4..5....4..1..6....4..6..2....4..2..5
..5..3..4....2..6..2....3..5..6....2..2..3....6..3..4....0..4..2....7..1..6
..4..2..5....0..6..0....3..3..0....5..5..4....0..5..2....7..3..5....2..4..3
..1..7..0....2..6..2....1..7..4....3..1..4....3..6..1....0..4..2....1..7..0
..2..4..3....2..4..2....3..3..0....6..4..5....2..3..4....4..6..2....1..5..2

Mathematica

A183675[n_] := 8*8^n + 42*7^n + 72*6^n + 90*5^n + 96*4^n + 90*3^n + 72*2^n + 42;
Array[A183675, 25] (* Paolo Xausa, Jun 18 2026 *)

Crossrefs

Column 2 of A183680.

Sequence in context: A180921 A270537 A076581 * A178272 A194605 A233104

Adjacent sequences: A183672 A183673 A183674 * A183676 A183677 A183678

Keyword

nonn,easy,changed

Author

R. H. Hardin, Jan 06 2011

Status

approved