A235014 - OEIS

A235014

Number of (n+1) X (5+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 3, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

%I #9 Jun 19 2022 01:26:56

%S 1736,2568,4008,6856,12168,23016,44680,90824,189032,407880,900168,

%T 2043496,4730184,11179080,26815912,65246024,160397576,397950312,

%U 993981960,2496937288,6298923240,15945371592,40469357512,102926663144

%N Number of (n+1) X (5+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 3, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

%H R. H. Hardin, <a href="/A235014/b235014.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) + a(n-2) - 38*a(n-3) + 33*a(n-4) + 97*a(n-5) - 127*a(n-6) - 88*a(n-7) + 154*a(n-8) + 12*a(n-9) - 48*a(n-10).

%F Empirical g.f.: 8*x*(217 - 764*x - 1321*x^2 + 6277*x^3 + 1772*x^4 - 18189*x^5 + 2134*x^6 + 21334*x^7 - 4260*x^8 - 7872*x^9) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 3*x^2)*(1 - x - 4*x^2)). - _Colin Barker_, Oct 17 2018

%e Some solutions for n=4:

%e 2 0 2 1 2 0 1 0 2 4 3 2 0 2 1 2 0 4 4 3 2 4 2 3

%e 1 2 1 3 1 2 2 4 3 2 4 0 1 0 2 0 1 2 0 2 4 3 4 2

%e 3 1 3 2 3 1 1 0 2 4 3 2 2 4 3 4 2 0 2 1 0 2 0 1

%e 1 2 1 3 1 2 2 4 3 2 4 0 1 0 2 0 1 2 4 0 2 1 2 0

%e 2 0 2 1 2 0 1 0 2 4 3 2 0 2 1 2 0 4 2 1 0 2 0 1

%Y Column 5 of A235017.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 02 2014