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A264273 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 1,0 or 1,2.

%I A264273 #11 Jun 29 2023 11:30:18
%S A264273 9,48,256,1280,6400,32000,160000,800000,4000000,20000000,100000000,
%T A264273 500000000,2500000000,12500000000,62500000000,312500000000,
%U A264273 1562500000000,7812500000000,39062500000000,195312500000000,976562500000000
%N A264273 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 1,0 or 1,2.
%H A264273 R. H. Hardin, <a href="/A264273/b264273.txt">Table of n, a(n) for n = 1..210</a>
%H A264273 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (5).
%F A264273 Empirical: a(n) = 5*a(n-1) for n>3.
%F A264273 Conjectures from _Colin Barker_, Jan 07 2019: (Start)
%F A264273 G.f.: x*(9 + 3*x + 16*x^2) / (1 - 5*x).
%F A264273 a(n) = 256*5^(n-3) for n>2.
%F A264273 (End)
%e A264273 Some solutions for n=4:
%e A264273 ..7..1..9..8..4....5..8..9..3..4....5..1..2..3..4....7..1..2..3..4
%e A264273 .12.13..0..3..2....0.11..7..1..2....0.11..7.13..9....0.11.12..8.14
%e A264273 .10.11..5..6.14...10..6.12.13.14...10..6.12..8.14...10..6..5.13..9
%Y A264273 Row 2 of A264272.
%K A264273 nonn
%O A264273 1,1
%A A264273 _R. H. Hardin_, Nov 10 2015