A183674 - OEIS

%I #25 Jun 18 2026 09:31:28

%S 344,2080,13448,90784,631784,4497760,32592008,239551264,1781373224,

%T 13376585440,101278522568,772234051744,5923974485864,45683076481120,

%U 353896909605128,2752474657736224,21482113227489704,168170396980664800,1320011294944399688,10385300157636428704,81874665418413344744

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

%H R. H. Hardin, <a href="/A183674/b183674.txt">Table of n, a(n) for n = 1..189</a>

%H Christian Krause, <a href="/A183674/a183674.txt">Proof of formulas</a>, Jun 12 2026

%F 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).

%F 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

%F 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

%F 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

%e Some solutions for 3 X 2:

%e ..5..0....1..5....3..3....0..5....2..7....2..4....2..2....5..6....2..4....0..6

%e ..4..5....4..4....3..5....5..4....0..5....4..4....3..7....1..2....5..3....4..4

%e ..1..4....1..5....6..0....3..2....6..3....0..6....1..3....5..6....6..0....2..4

%t A183674[n_] := 8*8^n + 14*7^n + 12*6^n + 10*5^n + 8*4^n + 6*3^n + 4*2^n + 2;

%t Array[A183674, 25] (* _Paolo Xausa_, Jun 18 2026 *)

%Y Column 1 of A183680.

%K nonn,easy

%O 1,1

%A _R. H. Hardin_, Jan 06 2011