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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,-2.
1

%I #8 Jan 01 2024 18:44:19

%S 4,64,324,2025,15625,102400,692224,4826809,32867289,224820036,

%T 1544804416,10578122500,72482100625,496981290961,3405885014016,

%U 23343276294144,160005726539569,1096673231227249,7516662847716100,51520374361000000

%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,-2.

%C Column 3 of A264059.

%H R. H. Hardin, <a href="/A264055/b264055.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) -a(n-2) +55*a(n-3) -385*a(n-4) +55*a(n-5) -385*a(n-6) +2695*a(n-7) -385*a(n-8) +385*a(n-9) -2695*a(n-10) +385*a(n-11) -55*a(n-12) +385*a(n-13) -55*a(n-14) +a(n-15) -7*a(n-16) +a(n-17).

%e Some solutions for n=4

%e ..0..1..2..3....6..1..2..9....0..7..8..9....0..1..2..9....0..7..2..9

%e .10..5..6.13....4..5..0..7....4..5..6..1....4..5..6..7....4..5..6..1

%e ..8..9..4.17....8..3.16.17....2..3.10.17....8..3.10.17...14..3.16.17

%e .18..7.14.15...18.13.14.15...12.19.14.15...18.19.14.15...12.19..8.15

%e .16.11.12.19...10.11.12.19...16.11.18.13...16.11.12.13...10.11.18.13

%Y Cf. A264059.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 02 2015