%I #8 Jan 01 2024 18:44:19
%S 4,64,324,2025,15625,102400,692224,4826809,32867289,224820036,
%T 1544804416,10578122500,72482100625,496981290961,3405885014016,
%U 23343276294144,160005726539569,1096673231227249,7516662847716100,51520374361000000
%N Number of (n+1) X (3+1) arrays of permutations of 0..n*4+3 with each element having index change +-(.,.) 0,0 1,2 or 2,-2.
%C Column 3 of A264059.
%H R. H. Hardin, <a href="/A264055/b264055.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 7*a(n-1) -a(n-2) +55*a(n-3) -385*a(n-4) +55*a(n-5) -385*a(n-6) +2695*a(n-7) -385*a(n-8) +385*a(n-9) -2695*a(n-10) +385*a(n-11) -55*a(n-12) +385*a(n-13) -55*a(n-14) +a(n-15) -7*a(n-16) +a(n-17).
%e Some solutions for n=4
%e ..0..1..2..3....6..1..2..9....0..7..8..9....0..1..2..9....0..7..2..9
%e .10..5..6.13....4..5..0..7....4..5..6..1....4..5..6..7....4..5..6..1
%e ..8..9..4.17....8..3.16.17....2..3.10.17....8..3.10.17...14..3.16.17
%e .18..7.14.15...18.13.14.15...12.19.14.15...18.19.14.15...12.19..8.15
%e .16.11.12.19...10.11.12.19...16.11.18.13...16.11.12.13...10.11.18.13
%Y Cf. A264059.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 02 2015