A202545 - OEIS

%I #8 Jun 01 2018 09:53:11

%S 1,8,86,1094,15184,219934,3249298,48427802,724492208,10855670258,

%T 162764756218,2441054713126,36613379378704,549186530733206,

%U 8237716581278546,123565284853121186,1853476648287687712

%N Number of n X 4 nonnegative integer arrays each row and column an ascent sequence (interior element no greater than one plus up-steps preceding it).

%C Column 4 of A202549.

%H R. H. Hardin, <a href="/A202545/b202545.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 36*a(n-1) -492*a(n-2) +3418*a(n-3) -13215*a(n-4) +28650*a(n-5) -32500*a(n-6) +15000*a(n-7).

%F Empirical g.f.: x*(1 - 28*x + 290*x^2 - 1484*x^3 + 3983*x^4 - 5320*x^5 + 2700*x^6) / ((1 - 2*x)^3*(1 - 5*x)^3*(1 - 15*x)). - _Colin Barker_, Jun 01 2018

%e Some solutions for n=5:

%e ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0

%e ..0..1..1..1....0..1..1..0....0..0..0..0....0..1..1..1....0..1..1..1

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

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

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

%Y Cf. A202549.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 20 2011