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A264072 Number of (3+1) X (n+1) arrays of permutations of 0..n*4+3 with each element having index change +-(.,.) 0,0 1,1 or 1,2.

%I A264072 #12 Mar 26 2025 18:45:16
%S A264072 8,89,1210,12100,131890,1445345,15892745,174807490,1922750500,
%T A264072 21148816810,232621218005,2558660023205,28143353265610,
%U A264072 309555910473700,3404884300976290,37451189626157945,411935173248700145,4530979887509803090,49837401790945888900,548174275529004512410
%N A264072 Number of (3+1) X (n+1) arrays of permutations of 0..n*4+3 with each element having index change +-(.,.) 0,0 1,1 or 1,2.
%H A264072 R. H. Hardin, <a href="/A264072/b264072.txt">Table of n, a(n) for n = 1..210</a>
%F A264072 Empirical: a(n) = 12*a(n-1) - 12*a(n-2) + 12*a(n-3) - 12*a(n-4) + a(n-5) for n>7.
%F A264072 Empirical g.f.: x*(8 - 7*x + 238*x^2 - 1448*x^3 + 238*x^4 - 5595*x^5 + 516*x^6) / ((1 - x)*(1 - 11*x + x^2 - 11*x^3 + x^4)). - _Colin Barker_, Jan 04 2019
%e A264072 Some solutions for n=4:
%e A264072 ..7..1..2..9..4....0..7..9..3..4....0..1..2..3..4....6..1..2..3..4
%e A264072 ..5.12..0..8..3....5..6.14..1..2...11.13..7.14..9...12.13..0..8..9
%e A264072 .17.18.19..6.14...17.11.18.13..8...16..5.18..6..8...10.17..5..7.14
%e A264072 .15.16.10.11.13...15.16.10.12.19...15.10.17.12.19...15.16.11.18.19
%Y A264072 Row 3 of A264071.
%K A264072 nonn
%O A264072 1,1
%A A264072 _R. H. Hardin_, Nov 02 2015