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

%I #8 Apr 02 2018 08:28:49

%S 16626,43986,135966,469146,1755246,6990906,29275086,127755066,

%T 577190766,2686295226,12829230606,62680963386,312535936686,

%U 1587207989946,8196463880526,42981002402106,228591556161006,1231705534203066

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

%C Column 4 of A183662.

%H R. H. Hardin, <a href="/A183657/b183657.txt">Table of n, a(n) for n = 1..163</a>

%F Empirical: 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).

%F Empirical g.f.: 6*x*(2771 - 50860*x + 353635*x^2 - 1151450*x^3 + 1728024*x^4 - 933120*x^5) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)). - _Colin Barker_, Apr 02 2018

%e Some solutions for 3 X 5:

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

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

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

%Y Cf. A183662.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 06 2011