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A264337 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

%I A264337 #8 Jan 07 2019 11:17:22
%S A264337 181,3567,70669,1399783,27726581,549201567,10878455069,215477871383,
%T A264337 4268134837381,84542207852367,1674592106593069,33169925350906183,
%U A264337 657022055372706581,13014137857695923967,257780972182185860669
%N A264337 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having index change +-(.,.) 0,0 0,1 or 1,2.
%H A264337 R. H. Hardin, <a href="/A264337/b264337.txt">Table of n, a(n) for n = 1..210</a>
%F A264337 Empirical: a(n) = 19*a(n-1) + 16*a(n-2).
%F A264337 Conjectures from _Colin Barker_, Jan 07 2019: (Start)
%F A264337 G.f.: x*(181 + 128*x) / (1 - 19*x - 16*x^2).
%F A264337 a(n) = (2^(-n)*((19-5*sqrt(17))^n*(-21+4*sqrt(17)) + (21+4*sqrt(17))*(19+5*sqrt(17))^n)) / sqrt(17).
%F A264337 (End)
%e A264337 Some solutions for n=3:
%e A264337 ..0..2..1..4..3....0..8..1..3..4....7..1..3..2..4....0..2..1..4..3
%e A264337 .12..6..7..9..8...12..5..7..9..2....5.13..0..8..9....5..6.14..9..8
%e A264337 .17.10..5.14.13...17.11.13..6.14...11.10.12..6.14...11.10.12.13..7
%e A264337 .16.15.18.11.19...15.16.10.18.19...15.17.16.19.18...16.15.18.17.19
%Y A264337 Column 4 of A264341.
%K A264337 nonn
%O A264337 1,1
%A A264337 _R. H. Hardin_, Nov 11 2015