A251367 - OEIS

%I #12 Mar 20 2018 00:55:46

%S 695,17969,464393,12002283,310199103,8017100977,207202101873,

%T 5355141623323,138403720518311,3577046360518609,92448820142650873,

%U 2389341228591410219,61752562096926105327,1595995950642355498897

%N 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 Column 2 of A251373.

%H R. H. Hardin, <a href="/A251367/b251367.txt">Table of n, a(n) for n = 1..210</a>

%H Robert Israel, <a href="/A251367/a251367.pdf">Maple-assisted proof of empirical formula</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (24,49,-34).

%F Empirical: a(n) = 24*a(n-1) + 49*a(n-2) - 34*a(n-3).

%F From _Robert Israel_, Mar 19 2018: (Start)

%F Empirical formula verified: see link.

%F G.f.: (695*x+1289*x^2-918*x^3)/(1-24*x-49*x^2+34*x^3). (End)

%e Some solutions for n=2:

%e   2 1 1   2 0 2   0 2 1   2 2 2   0 0 2   0 0 2   0 0 2

%e   0 0 0   1 0 0   1 0 1   0 1 1   1 1 2   1 2 1   1 1 1

%e   1 2 2   2 0 1   1 2 1   2 0 2   0 0 1   1 0 1   0 1 0

%p 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 map(f, [$1..30]); # _Robert Israel_, Mar 19 2018

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 01 2014