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A264874 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change 0,1 0,-1 -2,0 or 1,1.

%I A264874 #4 Nov 27 2015 07:31:10
%S A264874 1,1,5,20,56,137,295,709,1983,5280,13521,34173,85993,219721,567894,
%T A264874 1461417,3737198,9546206,24410323,62518425,160259301,410562684,
%U A264874 1050999521,2690293140,6888161028,17639430568,45173289641,115675667529
%N A264874 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change 0,1 0,-1 -2,0 or 1,1.
%C A264874 Column 3 of A264878.
%H A264874 R. H. Hardin, <a href="/A264874/b264874.txt">Table of n, a(n) for n = 1..210</a>
%F A264874 Empirical: a(n) = a(n-1) +5*a(n-3) +4*a(n-4) +21*a(n-5) +21*a(n-6) +13*a(n-7) -58*a(n-8) -70*a(n-9) -157*a(n-10) -198*a(n-11) -102*a(n-12) +209*a(n-13) +273*a(n-14) +553*a(n-15) +594*a(n-16) +289*a(n-17) -359*a(n-18) -430*a(n-19) -917*a(n-20) -765*a(n-21) -338*a(n-22) +401*a(n-23) +387*a(n-24) +812*a(n-25) +551*a(n-26) +167*a(n-27) -301*a(n-28) -174*a(n-29) -444*a(n-30) -208*a(n-31) -21*a(n-32) +107*a(n-33) +37*a(n-34) +134*a(n-35) +34*a(n-36) -17*a(n-38) -3*a(n-39) -19*a(n-40) -2*a(n-41) +a(n-43) +a(n-45)
%e A264874 Some solutions for n=4
%e A264874 ..1..2..3.11....1..0..3.11....1..2..3.11....1..2..3.11....1..0..3..2
%e A264874 .12..0..7.15....5..4..7..2...12..0..7..6....5..0..7.15....5..4..7.15
%e A264874 .16..4..5..6...16..8..9..6....9..4..5.10...16..4.18..6...16..8.11..6
%e A264874 .13..8..9.10...13.12.15.10...13..8.15.14...13..8..9.10...13.12..9.10
%e A264874 .17.18.19.14...17.18.19.14...17.16.19.18...17.12.19.14...17.18.19.14
%Y A264874 Cf. A264878.
%K A264874 nonn
%O A264874 1,3
%A A264874 _R. H. Hardin_, Nov 27 2015