cp's OEIS Frontend

A250653 Number of (n+1)X(5+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

%I A250653 #10 Jul 23 2025 12:39:28
%S A250653 49,103,211,427,859,1723,3451,6907,13819,27643,55291,110587,221179,
%T A250653 442363,884731,1769467,3538939,7077883,14155771,28311547,56623099,
%U A250653 113246203,226492411,452984827,905969659,1811939323,3623878651
%N A250653 Number of (n+1)X(5+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.
%C A250653 Column 5 of A250656.
%C A250653 Since one edge length of the array is fixed, and the constraint is a Markov-type correlation between fixed-width lengths of the other edge, the generating function is computable by the usual transfer matrix method and therefore a rational polynomial. That predicts that there is a linear recurrence. - _R. J. Mathar_, May 25 2018
%H A250653 R. H. Hardin, <a href="/A250653/b250653.txt">Table of n, a(n) for n = 1..210</a>
%F A250653 Empirical: a(n) = 3*a(n-1) - 2*a(n-2); also a(n) = 2^(n-1)*25 + (5*2^(n-1)-1)*5 + 2^(n+1).
%F A250653 It appears that a(n) = 27*2^n-5, which would make this coincide with A304387. - _N. J. A. Sloane_, May 13 2018
%e A250653 Some solutions for n=4
%e A250653 ..1..1..1..0..0..0....1..1..1..1..1..1....1..1..1..1..1..1....1..1..1..1..0..0
%e A250653 ..0..0..0..0..0..0....1..1..1..1..1..1....1..1..1..1..1..1....0..0..0..0..0..0
%e A250653 ..1..1..1..1..1..1....0..0..0..0..0..0....0..0..0..0..0..0....1..1..1..1..1..1
%e A250653 ..1..1..1..1..1..1....0..0..0..0..0..0....0..0..0..0..0..0....1..1..1..1..1..1
%e A250653 ..0..0..0..0..1..1....1..1..1..1..1..1....0..0..0..0..1..1....0..0..0..1..1..1
%Y A250653 Cf. A304387.
%K A250653 nonn
%O A250653 1,1
%A A250653 _R. H. Hardin_, Nov 26 2014