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A264068 Number of (n+1) X (5+1) arrays of permutations of 0..n*6+5 with each element having index change +-(.,.) 0,0 1,1 or 1,2.

%I A264068 #12 Mar 26 2025 18:44:49
%S A264068 89,3025,131890,5645376,242621698,10427064769,448121165789,
%T A264068 19258783041289,827679549612058,35570961850254336,1528723680011326810,
%U A264068 65699547278636775625,2823551809301370027485,121347028252680274383361,5215098663055950428459458,224127895483153188149350464
%N A264068 Number of (n+1) X (5+1) arrays of permutations of 0..n*6+5 with each element having index change +-(.,.) 0,0 1,1 or 1,2.
%H A264068 R. H. Hardin, <a href="/A264068/b264068.txt">Table of n, a(n) for n = 1..210</a>
%F A264068 Empirical: a(n) = 43*a(n-1) - 43*a(n-3) + a(n-4) for n>5.
%F A264068 Empirical g.f.: x*(89 - 802*x + 1815*x^2 - 22067*x^3 + 516*x^4) / ((1 - x)*(1 + x)*(1 - 43*x + x^2)). - _Colin Barker_, Jan 04 2019
%e A264068 Some solutions for n=3:
%e A264068 ..0..8.10..3.11..5....8..1..2.10..4..5....0..8..2..3.11..5....7..1.10..3.11..5
%e A264068 .13.15..1..2.17..4....6.15..0.16..3.11...14..7..1..9.10..4....6..0.15..2.17..4
%e A264068 .12..6.22..7.16..9...19.13.21..7..9.17...20.21..6.15.23.17...19.13.22..8.16..9
%e A264068 .18.19.20.21.14.23...18.12.20.14.22.23...18.19.12.13.22.16...18.12.20.21.14.23
%Y A264068 Column 5 of A264071.
%K A264068 nonn
%O A264068 1,1
%A A264068 _R. H. Hardin_, Nov 02 2015