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 A264529 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change -2,-2 -1,0 0,1 or 1,0. 1

%I #4 Nov 17 2015 09:23:39

%S 1,2,13,40,229,696,3273,12832,52897,209890,848673,3410748,13734005,

%T 55435856,222621989,897990076,3610748165,14552830034,58558270001,

%U 235878435500,949470694545,3823609350504,15393910820101,61985526413732

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

%C Column 3 of A264534.

%H R. H. Hardin, <a href="/A264529/b264529.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) +13*a(n-2) -60*a(n-3) -42*a(n-4) +392*a(n-5) -102*a(n-6) -1668*a(n-7) +1431*a(n-8) +7740*a(n-9) -12835*a(n-10) -31952*a(n-11) +73992*a(n-12) +92400*a(n-13) -275368*a(n-14) -173104*a(n-15) +697118*a(n-16) +203576*a(n-17) -1254966*a(n-18) -135080*a(n-19) +1665556*a(n-20) -1665556*a(n-22) +135080*a(n-23) +1254966*a(n-24) -203576*a(n-25) -697118*a(n-26) +173104*a(n-27) +275368*a(n-28) -92400*a(n-29) -73992*a(n-30) +31952*a(n-31) +12835*a(n-32) -7740*a(n-33) -1431*a(n-34) +1668*a(n-35) +102*a(n-36) -392*a(n-37) +42*a(n-38) +60*a(n-39) -13*a(n-40) -4*a(n-41) +a(n-42)

%e Some solutions for n=4

%e ..4.11..6..2....4.11..1..2...10.11..6..7....4.11..6..2...10..0..6..2

%e ..0..1..5..3....0..9..5..3....0..1..2..3....0..1..5..3....8..1..5..3

%e .18.13..9..7...18..8..6..7....4..5.14.15...18..8..9..7....4.19..9..7

%e ..8.17.10.19...16.17.10.19....8..9.13.19...16.17.10.19...16.17.18.11

%e .12.16.14.15...12.13.14.15...12.16.17.18...12.13.14.15...12.13.14.15

%Y Cf. A264534.

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 17 2015

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