A234876 - OEIS

A234876

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

%I #10 Jun 19 2022 01:16:44

%S 68,148,268,628,1188,2944,5684,14604,28492,74816,146772,390308,767956,

%T 2057064,4053820,10903852,21506484,57986664,114425348,308952828,

%U 609818236,1647911016,3253169924,8795476020,17364799332,46963065504

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

%H R. H. Hardin, <a href="/A234876/b234876.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 10*a(n-2) - 21*a(n-3) - 29*a(n-4) + 68*a(n-5) + 22*a(n-6) - 73*a(n-7) + 22*a(n-9).

%F Empirical g.f.: 4*x*(17 + 3*x - 177*x^2 + 10*x^3 + 583*x^4 - 104*x^5 - 671*x^6 + 110*x^7 + 231*x^8) / ((1 - x)*(1 - x - x^2)*(1 - 10*x^2 + 29*x^4 - 22*x^6)). - _Colin Barker_, Oct 16 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 2 of A234882.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 01 2014