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A264281 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change 0,0 0,1 1,0 or -1,-2.

%I A264281 #8 Jan 07 2019 06:09:06
%S A264281 16,102,675,4484,29742,197283,1308629,8680430,57579243,381936079,
%T A264281 2533467942,16805062848,111471762753,739417281750,4904721187204,
%U A264281 32534119120513,215806131795839,1431490625216236,9495399380127733
%N A264281 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change 0,0 0,1 1,0 or -1,-2.
%H A264281 R. H. Hardin, <a href="/A264281/b264281.txt">Table of n, a(n) for n = 1..210</a>
%F A264281 Empirical: a(n) = 7*a(n-1) - 2*a(n-2) - 2*a(n-3) - 6*a(n-4) + a(n-5) + 3*a(n-6).
%F A264281 Empirical g.f.: x*(16 - 10*x - 7*x^2 - 5*x^3 + 4*x^4 + 3*x^5) / ((1 - x)*(1 - 6*x - 4*x^2 - 2*x^3 + 4*x^4 + 3*x^5)). - _Colin Barker_, Jan 07 2019
%e A264281 Some solutions for n=4:
%e A264281 ..7..1..9..2..4....0..1..2..3..4....0..8..1..2..4....0..1..2..3..4
%e A264281 ..0..6.14..3..8...12.13..6..7..9...12..6..7..3..9....5..6.14..7..9
%e A264281 ..5.10.11.12.13....5.18.11..8.14....5.10.11.13.14...10.11.12..8.13
%e A264281 .22.16.24.17.18...10.15.16.17.19...15.16.24.18.19...22.16.24.17.18
%e A264281 .15.20.21.23.19...20.21.22.23.24...20.21.17.22.23...15.20.21.23.19
%Y A264281 Column 4 of A264285.
%K A264281 nonn
%O A264281 1,1
%A A264281 _R. H. Hardin_, Nov 10 2015