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A264564 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

%I A264564 #4 Nov 17 2015 19:08:28
%S A264564 1,4,10,31,79,224,646,1784,5010,14026,39283,110214,308476,864321,
%T A264564 2421872,6784237,19008032,53250952,149186453,417966045,1170955616,
%U A264564 3280543940,9190733824,25748605578,72137045260,202098106485,566195445452
%N A264564 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change 1,0 1,1 0,-1 or -1,1.
%C A264564 Column 3 of A264569.
%H A264564 R. H. Hardin, <a href="/A264564/b264564.txt">Table of n, a(n) for n = 1..210</a>
%F A264564 Empirical: a(n) = 2*a(n-1) +a(n-2) +6*a(n-3) -6*a(n-4) +6*a(n-5) -27*a(n-6) +5*a(n-7) -9*a(n-8) +33*a(n-9) -4*a(n-10) +7*a(n-11) -12*a(n-12) +a(n-13) -a(n-14) +a(n-15)
%e A264564 Some solutions for n=4
%e A264564 ..1..4..3..6....1..4..3..6....1..4..3..6....1..2..5..6....1..2..5..6
%e A264564 ..5..0..7..2....5..0..2.10....5..0..7..2....0..8..7..3....0..8..7..3
%e A264564 ..9.12.13.14....9.12.13..7....9.10.11.14....9..4.11.14....9..4.11.14
%e A264564 ..8.16.10.11....8.16.15.11....8.16.17.18...13.16.17.10...13.16.10.18
%e A264564 .17.18.19.15...17.18.19.14...12.13.19.15...12.18.19.15...17.12.19.15
%Y A264564 Cf. A264569.
%K A264564 nonn
%O A264564 1,2
%A A264564 _R. H. Hardin_, Nov 17 2015