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A251366 Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock summing to 1 2 3 4 5 6 or 7.

%I A251366 #21 Aug 20 2022 10:49:14
%S A251366 79,695,6113,53769,472943,4159927,36590017,321839625,2830847119,
%T A251366 24899654327,219013164449,1926402895881,16944315318191,
%U A251366 149039342816695,1310924949760897,11530674997804041,101421874630758607
%N A251366 Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock summing to 1 2 3 4 5 6 or 7.
%C A251366 Column 1 of A251373.
%H A251366 R. H. Hardin, <a href="/A251366/b251366.txt">Table of n, a(n) for n = 1..210</a>
%H A251366 Robert Israel, <a href="/A251366/a251366.pdf">Maple-assisted proof of formula</a>
%H A251366 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,7).
%F A251366 Empirical: a(n) = 8*a(n-1) + 7*a(n-2).
%F A251366 Empirical g.f.: x*(79 + 63*x) / (1 - 8*x - 7*x^2). - _Colin Barker_, Mar 19 2018
%F A251366 Empirical formula verified: see link.
%F A251366 a(n) = A254598(n+1). - _Robert Israel_, Mar 19 2018
%e A251366 Some solutions for n=4:
%e A251366   1 1   0 1   1 2   2 1   1 2   2 1   0 0   2 1   1 0   0 2
%e A251366   2 2   0 2   1 0   0 1   2 0   2 2   0 1   2 2   0 0   0 1
%e A251366   2 1   1 1   0 1   1 2   2 2   1 1   2 0   2 1   1 2   0 2
%e A251366   2 1   2 0   1 2   1 0   1 0   1 2   1 1   2 1   0 2   2 2
%e A251366   0 1   1 0   0 0   1 1   1 1   0 0   1 0   1 1   0 1   0 2
%p A251366 f:= gfun:-rectoproc({a(n) = 8*a(n-1) + 7*a(n-2), a(1)=
%p A251366 79, a(2)=695},a(n),remember):
%p A251366 map(f, [$1..40]); # _Robert Israel_, Mar 19 2018
%t A251366 LinearRecurrence[{8, 7}, {79, 695}, 40] (* _Jean-François Alcover_, Aug 19 2022 *)
%Y A251366 Cf. A251373, A254598.
%K A251366 nonn,easy
%O A251366 1,1
%A A251366 _R. H. Hardin_, Dec 01 2014