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A264060 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 1,2 or 2,-2.

%I A264060 #8 Mar 15 2023 14:58:57
%S A264060 1,8,64,216,729,3375,15625,64000,262144,1124864,4826809,20346417,
%T A264060 85766121,363994344,1544804416,6539203000,27680640625,117289217375,
%U A264060 496981290961,2105026154496,8916100448256,37770717892608,160005726539569
%N A264060 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 1,2 or 2,-2.
%C A264060 Row 2 of A264059.
%H A264060 R. H. Hardin, <a href="/A264060/b264060.txt">Table of n, a(n) for n = 1..210</a>
%F A264060 Empirical: a(n) = 4*a(n-1) -4*a(n-2) +20*a(n-3) +20*a(n-4) -60*a(n-5) -60*a(n-7) -20*a(n-8) +20*a(n-9) +4*a(n-10) +4*a(n-11) +a(n-12).
%e A264060 Some solutions for n=4
%e A264060 ..0..1..2.11..4....7..1..2..3..4....7..8.10.11.12....0..1.10..3..4
%e A264060 ..5..6.14..8..9...12..6..0..8..9....5..6..0..1..9....5..6.14..8..9
%e A264060 .10..3.12.13..7...10.11..5.13.14....2..3..4.13.14....2.11.12.13..7
%Y A264060 Cf. A264059.
%K A264060 nonn
%O A264060 1,2
%A A264060 _R. H. Hardin_, Nov 02 2015