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A264212 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change 0,0 0,1 1,0 -1,0 or 0,-2. 1

%I #6 Nov 10 2015 11:39:45

%S 56,623,7949,97520,1210573,14973263,185410184,2295059475,28412159649,

%T 351721081216,4354093505569,53900825368787,667257749134088,

%U 8260220853354511,102256223622663277,1265866252726331184

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

%C Column 3 of A264217.

%H R. H. Hardin, <a href="/A264212/b264212.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 17*a(n-1) -43*a(n-2) -285*a(n-3) +1433*a(n-4) -479*a(n-5) -7539*a(n-6) +12721*a(n-7) +3719*a(n-8) -22631*a(n-9) -5279*a(n-10) +61275*a(n-11) -61275*a(n-12) +5279*a(n-13) +22631*a(n-14) -3719*a(n-15) -12721*a(n-16) +7539*a(n-17) +479*a(n-18) -1433*a(n-19) +285*a(n-20) +43*a(n-21) -17*a(n-22) +a(n-23)

%e Some solutions for n=4

%e ..4..1..6..3....0..3..2..7....4..3..1..2....0..3..1..2....0..5..2..7

%e ..0..9..2..7....4..1.10..6....0..9..5..6....4..5..6.11....4..1..6..3

%e ..8..5.10.15....8..5..9.15...10.13.14..7...12..8.14..7....8..9.10.15

%e .16.13.14.11...12.17.13.11....8.15.18.11...16..9.10.19...16.17.14.11

%e .12.19.17.18...16.19.14.18...12.16.17.19...18.13.17.15...12.13.18.19

%Y Cf. A264217.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 08 2015

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