A235241 - OEIS

A235241

Number of (n+1) X (1+1) 0..7 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 6, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

%I #11 Jun 19 2022 00:00:56

%S 210,906,3746,16150,66874,288510,1195458,5161934,21400266,92486622,

%T 383623154,1659369022,6886195834,29811968622,123773981922,

%U 536299705358,2227615662378,9660029955390,40141785286994,174215753195230

%N Number of (n+1) X (1+1) 0..7 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 6, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

%H R. H. Hardin, <a href="/A235241/b235241.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + 39*a(n-2) - 152*a(n-3) - 441*a(n-4) + 1612*a(n-5) + 1185*a(n-6) - 3128*a(n-7) - 782*a(n-8).

%F Empirical g.f.: 2*x*(105 + 33*x - 4034*x^2 - 1124*x^3 + 43251*x^4 + 10791*x^5 - 84602*x^6 - 20036*x^7) / ((1 - 4*x - x^2)*(1 - 17*x^2)*(1 - 21*x^2 + 46*x^4)). - _Colin Barker_, Oct 17 2018

%e Some solutions for n=4:

%e 4 1 0 1 3 7 5 7 4 6 6 2 5 6 4 7 4 2 4 2

%e 1 4 5 0 6 4 7 3 5 1 1 3 7 2 5 2 3 7 3 7

%e 3 0 6 7 3 7 4 6 2 4 4 0 5 6 2 5 2 0 7 5

%e 1 4 7 2 2 0 5 1 6 2 2 4 7 2 4 1 3 7 2 6

%e 3 0 6 7 1 5 0 2 1 3 4 0 0 1 2 5 4 2 4 2

%Y Column 1 of A235248.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 05 2014