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A264359 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change 0,0 0,2 1,0 or -1,-2.

%I A264359 #8 Dec 09 2015 06:30:21
%S A264359 9,36,169,784,3600,16641,76729,354025,1633284,7535025,34762816,
%T A264359 160376896,739894401,3413480625,15747991081,72652889764,335181944601,
%U A264359 1546351938576,7134048689296,32912721515521,151841862142569,700517916355401
%N A264359 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change 0,0 0,2 1,0 or -1,-2.
%C A264359 Column 3 of A264364.
%H A264359 R. H. Hardin, <a href="/A264359/b264359.txt">Table of n, a(n) for n = 1..210</a>
%F A264359 Empirical: a(n) = 3*a(n-1) +7*a(n-2) +3*a(n-3) -5*a(n-4) +3*a(n-5) -a(n-6).
%F A264359 Empirical G.f.: -x*(-9-9*x+2*x^2+2*x^3-2*x^4+x^5) / ( (x^3 -x^2 -2*x-1) *(x^3-2*x^2+5*x-1) ). - _R. J. Mathar_, Dec 09 2015
%e A264359 Some solutions for n=4
%e A264359 ..6..7..0..1....0..7..2..3....0..1..2..3....6..7..0..1....0..1..2..3
%e A264359 .10..5..2..3....4..1..6..5...10.11..4..7...10..5..2..3...10..5..6..7
%e A264359 ..4.15..8..9....8..9.10.11....8..5..6..9....4..9..8.11....4.15..8..9
%e A264359 .18.19.12.11...18.19.12.13...18.19.12.13...18.19.14.15...18.13.12.11
%e A264359 .16.13.14.17...16.17.14.15...16.17.14.15...12.13.16.17...16.17.14.19
%Y A264359 Cf. A264364.
%K A264359 nonn
%O A264359 1,1
%A A264359 _R. H. Hardin_, Nov 12 2015