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A264019 Number of (4+1) X (n+1) arrays of permutations of 0..n*5+4 with each element having index change +-(.,.) 0,0 1,2 or 2,2.

%I A264019 #9 Jan 03 2019 14:33:07
%S A264019 1,34,1156,20570,366025,7320500,146410000,2898918000,57398576400,
%T A264019 1136955639600,22520909184400,446088564737200,8836011280003600,
%U A264019 175021631355863600,3466787272192723600,68669304273355566000
%N A264019 Number of (4+1) X (n+1) arrays of permutations of 0..n*5+4 with each element having index change +-(.,.) 0,0 1,2 or 2,2.
%H A264019 R. H. Hardin, <a href="/A264019/b264019.txt">Table of n, a(n) for n = 1..210</a>
%F A264019 Empirical: a(n) = 19*a(n-1) + 304*a(n-3) + 256*a(n-4) for n>8.
%F A264019 Empirical g.f.: x*(1 + 15*x + 510*x^2 - 1698*x^3 - 35397*x^4 + 5897*x^5 + 771284*x^6 + 590480*x^7) / ((1 + 16*x^2)*(1 - 19*x - 16*x^2)). - _Colin Barker_, Jan 03 2019
%e A264019 Some solutions for n=4:
%e A264019 ..7..8..2..3..4....7..8..9..3..4....7..8..2..3..4....0..1..2..3..4
%e A264019 ..5.13.19..1..9...17.13.19..1..2...17.13..0..1..9....5.13.14..8..9
%e A264019 .10.11..0..6.14...10.23..0..6.14...22.23.12..6.14...10.11.24..6..7
%e A264019 .15.23.24.18.12...22.16..5.18.12...15.16..5.18.19...15.16.17.18.19
%e A264019 .20.21.22.16.17...20.21.15.11.24...20.21.10.11.24...20.21.22.23.12
%Y A264019 Row 4 of A264017.
%K A264019 nonn
%O A264019 1,2
%A A264019 _R. H. Hardin_, Nov 01 2015