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A251367 Number of (n+1) X (2+1) 0..2 arrays with every 2 X 2 subblock summing to 1, 2, 3, 4, 5, 6, or 7.

%I A251367 #12 Mar 20 2018 00:55:46
%S A251367 695,17969,464393,12002283,310199103,8017100977,207202101873,
%T A251367 5355141623323,138403720518311,3577046360518609,92448820142650873,
%U A251367 2389341228591410219,61752562096926105327,1595995950642355498897
%N A251367 Number of (n+1) X (2+1) 0..2 arrays with every 2 X 2 subblock summing to 1, 2, 3, 4, 5, 6, or 7.
%C A251367 Column 2 of A251373.
%H A251367 R. H. Hardin, <a href="/A251367/b251367.txt">Table of n, a(n) for n = 1..210</a>
%H A251367 Robert Israel, <a href="/A251367/a251367.pdf">Maple-assisted proof of empirical formula</a>
%H A251367 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (24,49,-34).
%F A251367 Empirical: a(n) = 24*a(n-1) + 49*a(n-2) - 34*a(n-3).
%F A251367 From _Robert Israel_, Mar 19 2018: (Start)
%F A251367 Empirical formula verified: see link.
%F A251367 G.f.: (695*x+1289*x^2-918*x^3)/(1-24*x-49*x^2+34*x^3). (End)
%e A251367 Some solutions for n=2:
%e A251367   2 1 1   2 0 2   0 2 1   2 2 2   0 0 2   0 0 2   0 0 2
%e A251367   0 0 0   1 0 0   1 0 1   0 1 1   1 1 2   1 2 1   1 1 1
%e A251367   1 2 2   2 0 1   1 2 1   2 0 2   0 0 1   1 0 1   0 1 0
%p A251367 f:= gfun:-rectoproc({a(n) = 24*a(n-1) +49*a(n-2) -34*a(n-3),a(1)=695,a(2)=17969, a(3)=464393},a(n),remember):
%p A251367 map(f, [$1..30]); # _Robert Israel_, Mar 19 2018
%K A251367 nonn
%O A251367 1,1
%A A251367 _R. H. Hardin_, Dec 01 2014