A183674 Number of (n+1) X 2 0..7 arrays with every 2 X 2 subblock summing to 14.

344, 2080, 13448, 90784, 631784, 4497760, 32592008, 239551264, 1781373224, 13376585440, 101278522568, 772234051744, 5923974485864, 45683076481120, 353896909605128, 2752474657736224, 21482113227489704, 168170396980664800, 1320011294944399688, 10385300157636428704, 81874665418413344744

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..189

Christian Krause, Proof of formulas, Jun 12 2026

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*(43 - 1288*x + 15799*x^2 - 102256*x^3 + 374218*x^4 - 766288*x^5 + 801072*x^6 - 322560*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 02 2018

a(n) = 8*8^n + 14*7^n + 12*6^n + 10*5^n + 8*4^n + 6*3^n + 4*2^n + 2. - Christian Krause, Jun 12 2026

E.g.f.: 2*(4*exp(8*x) + 7*exp(7*x) + 6*exp(6*x) + 5*exp(5*x) + 4*exp(4*x) + 3*exp(3*x) + 2*exp(2*x) + exp(x) - 32). - Stefano Spezia, Jun 18 2026

Example

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

Mathematica

A183674[n_] := 8*8^n + 14*7^n + 12*6^n + 10*5^n + 8*4^n + 6*3^n + 4*2^n + 2;
Array[A183674, 25] (* Paolo Xausa, Jun 18 2026 *)

Crossrefs

Column 1 of A183680.

Sequence in context: A237378 A237243 A183680 * A245994 A246630 A250921

Adjacent sequences: A183671 A183672 A183673 * A183675 A183676 A183677

Keyword

nonn,easy,changed

Author

R. H. Hardin, Jan 06 2011

Status

approved