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A264546 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change -1,1 -1,2 1,0 or 0,-1.

%I A264546 #8 Jan 08 2019 19:00:39
%S A264546 1,16,36,216,1160,4640,23140,110592,501828,2390752,11231244,52348752,
%T A264546 246436064,1155790856,5415128884,25420656744,119225756880,
%U A264546 559133362408,2623138509120,12303725497848,57710528607716,270708963027848
%N A264546 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change -1,1 -1,2 1,0 or 0,-1.
%H A264546 R. H. Hardin, <a href="/A264546/b264546.txt">Table of n, a(n) for n = 1..210</a>
%F A264546 Empirical: a(n) = 9*a(n-2) + 54*a(n-3) + 60*a(n-4) - 54*a(n-5) - 279*a(n-6) - 270*a(n-7) + 64*a(n-8) - 864*a(n-9) - 1728*a(n-10) for n>11.
%F A264546 Empirical g.f.: x*(1 + 16*x + 27*x^2 + 18*x^3 - 88*x^4 - 154*x^5 + 19*x^6 - 90*x^7 - 628*x^8 - 72*x^9 + 192*x^10) / (1 - 9*x^2 - 54*x^3 - 60*x^4 + 54*x^5 + 279*x^6 + 270*x^7 - 64*x^8 + 864*x^9 + 1728*x^10). - _Colin Barker_, Jan 08 2019
%e A264546 Some solutions for n=4:
%e A264546 ..1..5..3..6..7....1..2..3..4..7....1..2..3..6..8....1..2..3..7..8
%e A264546 ..0.10..2..9..4....0.10..8..9.12....0.10.11.12..4....0.10.11..9..4
%e A264546 .11.12.15..8.18....5..6.15.14.18....5.15..7.17..9....5..6.13.14.18
%e A264546 .16.17.20.13.14...16.11.20.13.23...16.20.18.13.14...16.20.12.21.23
%e A264546 .21.22.23.24.19...21.22.17.24.19...21.22.23.24.19...15.22.17.24.19
%Y A264546 Column 4 of A264550.
%K A264546 nonn
%O A264546 1,2
%A A264546 _R. H. Hardin_, Nov 17 2015