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A264672 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change -1,-1 1,0 -1,-2 -2,-2 or 0,1.

%I A264672 #6 May 19 2023 07:38:56
%S A264672 1,29,123,890,6851,43131,291315,1980287,13199209,88670692,595721002,
%T A264672 3995710025,26820625288,180019819900,1208161823995,8108780202591,
%U A264672 54422802858380,365262503014440,2451492555516290,16453389631984472
%N A264672 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change -1,-1 1,0 -1,-2 -2,-2 or 0,1.
%C A264672 Column 4 of A264676.
%H A264672 R. H. Hardin, <a href="/A264672/b264672.txt">Table of n, a(n) for n = 1..210</a>
%F A264672 Empirical: a(n) = 3*a(n-1) +9*a(n-2) +106*a(n-3) +212*a(n-5) -1161*a(n-6) +560*a(n-7) -3942*a(n-8) -6220*a(n-9) +2684*a(n-10) -18488*a(n-11) +10184*a(n-12) +76448*a(n-13) +97808*a(n-14) +177984*a(n-15) +21920*a(n-16) +647104*a(n-17) +834688*a(n-18) +224000*a(n-19) +513280*a(n-20) -413184*a(n-21) +221952*a(n-22) -379392*a(n-23) +216576*a(n-24) +258048*a(n-25) -73728*a(n-26) for n>27.
%e A264672 Some solutions for n=4
%e A264672 .12..0..1..9..3....7..0..9..2..3....6..0..1..9..3...12..0..1..2..3
%e A264672 .11..5..2..7..4...12..1..6.14..4...12..5..2..7..4...17.18..6..7..4
%e A264672 .17..6.19..8.13....5.17.19..8.13...16.18.24..8.13....5.23.24..8..9
%e A264672 .10.22.16.24.14...10.11.16.24.18...10.11.23.17.14...10.11.16.13.14
%e A264672 .15.20.21.18.23...15.20.21.22.23...15.20.21.22.19...15.20.21.22.19
%Y A264672 Cf. A264676.
%K A264672 nonn
%O A264672 1,2
%A A264672 _R. H. Hardin_, Nov 20 2015