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A234816 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 6 (constant-stress 1 X 1 tilings). 1

%I #9 Jun 19 2022 01:13:46

%S 168,686,2380,9716,34092,139112,493348,2011808,7205628,29360336,

%T 106119940,432009296,1574462652,6403264112,23513001988,95527797008,

%U 353173605948,1433355470576,5331803584900,21616468994576,80854559348412

%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 6 (constant-stress 1 X 1 tilings).

%H R. H. Hardin, <a href="/A234816/b234816.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + 41*a(n-2) - 164*a(n-3) - 558*a(n-4) + 2232*a(n-5) + 2520*a(n-6) - 10080*a(n-7).

%F Empirical g.f.: 2*x*(84 + 7*x - 3626*x^2 - 189*x^3 + 51948*x^4 + 1260*x^5 - 246960*x^6) / ((1 - 4*x)*(1 - 12*x^2)*(1 - 14*x^2)*(1 - 15*x^2)). - _Colin Barker_, Oct 16 2018

%e Some solutions for n=5:

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

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

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

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

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

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

%Y Column 1 of A234823.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 31 2013

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)