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A264167 Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having directed index change 0,0 0,1 1,0 -2,-1 or -1,-2.

%I A264167 #11 Jan 05 2019 06:46:53
%S A264167 4,25,98,418,1862,8007,34539,149808,648436,2805250,12142877,52558637,
%T A264167 227471330,984523558,4261166714,18442796291,79822557139,345481774068,
%U A264167 1495286247768,6471776351478,28010620722521,121233307002413
%N A264167 Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having directed index change 0,0 0,1 1,0 -2,-1 or -1,-2.
%H A264167 R. H. Hardin, <a href="/A264167/b264167.txt">Table of n, a(n) for n = 1..210</a>
%F A264167 Empirical: a(n) = a(n-1) + 7*a(n-2) + 23*a(n-3) + 35*a(n-4) + 18*a(n-5) for n>7.
%F A264167 Empirical g.f.: x*(4 + 21*x + 45*x^2 + 53*x^3 + 43*x^4 + 18*x^5 + 4*x^6) / (1 - x - 7*x^2 - 23*x^3 - 35*x^4 - 18*x^5). - _Colin Barker_, Jan 05 2019
%e A264167 Some solutions for n=4:
%e A264167 ..5..1..2....5..8..1....5..0..1....7..0..1....0..8..1....7..0..1....5..0..1
%e A264167 ..0..3..4....0..3..2....3..4..2....3.11..2...10..3..2....3..4..2....8..4..2
%e A264167 .11..6..8....6..4..7....6..7..8....6..4..5...13..4..5...13..6..5....3.14..7
%e A264167 .14..7.10...14.10.11...14..9.10...14..9..8....6..7.11...14..9..8....6..9.10
%e A264167 ..9.12.13....9.12.13...12.13.11...12.10.13....9.12.14...12.10.11...12.13.11
%Y A264167 Column 2 of A264172.
%K A264167 nonn
%O A264167 1,1
%A A264167 _R. H. Hardin_, Nov 06 2015