A264123 - OEIS

%I #11 Jun 29 2023 11:23:22

%S 4,45,576,5733,53361,533610,5336100,53361000,533610000,5336100000,

%T 53361000000,533610000000,5336100000000,53361000000000,

%U 533610000000000,5336100000000000,53361000000000000,533610000000000000

%N Number of (n+1) X (3+1) arrays of permutations of 0..n*4+3 with each element having index change +-(.,.) 0,0 1,-2 or 2,-1.

%H R. H. Hardin, <a href="/A264123/b264123.txt">Table of n, a(n) for n = 1..210</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (10).

%F Empirical: a(n) = 10*a(n-1) for n>5.

%F Conjectures from _Colin Barker_, Jan 04 2019: (Start)

%F G.f.: x*(4 + 5*x + 126*x^2 - 27*x^3 - 3969*x^4) / (1 - 10*x).

%F a(n) = 53361*10^(n-5) for n>4.

%F (End)

%e Some solutions for n=4:

%e ..0..1..9..5....0..8..9..5....0..8..4.10....0..8..9..3....0..8..4..3

%e ..4..3..8..7....4.12.13..7....2.12..6..7....4..5.13.14....2.12..6..9

%e ..6..2.12.11....1..2..3.18....1.16..3.11....1..2.10.11....1..7.17.11

%e .10.13.16.15...10..6.14.17....5.13.14.17...12..6..7.17....5.13.14.15

%e .14.17.18.19...16.15.11.19....9.15.18.19...16.15.18.19...16.10.18.19

%Y Column 3 of A264128.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 03 2015