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A234170 Number of (n+1) X (1+1) 0..6 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 1 (constant-stress 1 X 1 tilings). 1

%I #14 Jun 20 2022 21:34:46

%S 448,4536,47936,517104,5630848,61624416,675750656,7420655424,

%T 81506779648,895774029696,9842817944576,108194841049344,

%U 1188960811214848,13069954464677376,143629781032349696,1578903606956196864

%N Number of (n+1) X (1+1) 0..6 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 1 (constant-stress 1 X 1 tilings).

%H R. H. Hardin, <a href="/A234170/b234170.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 154*a(n-2) - 4144*a(n-4) + 16176*a(n-6).

%F Empirical g.f.: 8*x*(56 + 567*x - 2632*x^2 - 22680*x^3 + 13152*x^4 + 98448*x^5) / (1 - 154*x^2 + 4144*x^4 - 16176*x^6). - _Colin Barker_, Oct 13 2018

%e Some solutions for n=3:

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

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

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

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

%Y Column 1 of A234175.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 20 2013

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