A250905 - OEIS

%I #10 Nov 23 2018 21:17:47

%S 40357,144442,412006,1052787,2553537,6060594,14283986,33622407,

%T 79146865,186303082,438524102,1032952851,2438864985,5785894874,

%U 13834474066,33456261815,82124660857,205298412354,524006897206,1367662361011

%N Number of (7+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

%H R. H. Hardin, <a href="/A250905/b250905.txt">Table of n, a(n) for n = 1..128</a>

%F Empirical: a(n) = 14*a(n-1) - 85*a(n-2) + 294*a(n-3) - 639*a(n-4) + 906*a(n-5) - 839*a(n-6) + 490*a(n-7) - 164*a(n-8) + 24*a(n-9).

%F Empirical g.f.: x*(40357 - 420556*x + 1820163*x^2 - 4302685*x^3 + 6157204*x^4 - 5596797*x^5 + 3233842*x^6 - 1077420*x^7 + 157464*x^8) / ((1 - x)^5*(1 - 2*x)^3*(1 - 3*x)). - _Colin Barker_, Nov 23 2018

%e Some solutions for n=2:

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

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

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

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

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

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

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

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

%Y Row 7 of A250898.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 28 2014