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%I #9 May 01 2013 09:01:18
%S 1,0,2,384,132000,79716000,78928416000,120481708032000,
%T 269702267433984000,850271305403520000000,3652393464869909760000000,
%U 20798525597035736309760000000,153427251286862484058423296000000,1437639344607855309441929920512000000
%N Number of lattice paths without interior points from {3}^n to {0}^n using steps that decrement one component by 1.
%C An interior point p = (p_1, ..., p_n) has n>0 components with 0<p_i<3 for 1<=i<=n.
%H Alois P. Heinz, <a href="/A225096/b225096.txt">Table of n, a(n) for n = 0..100</a>
%e a(0) = 1: [()].
%e a(1) = 0, there is no path from (3) to (0) without interior points.
%e a(2) = 2: [(3,3), (2,3), (1,3), (0,3), (0,2), (0,1), (0,0)], [(3,3), (3,2), (3,1), (3,0), (2,0), (1,0), (0,0)].
%p a:= proc(n) option remember; `if`(n<3, [1, 0, 2][n+1],
%p (2*(3*n-1)*(3*n-2)*(7*n^2-9*n-4)*n*a(n-1)
%p -3*n^2*(3*n-5)*(3*n-1)*(3*n-4)*(3*n-2)*(n-1)^2*a(n-2))/
%p (8*(2*n+1)*(n-2)))
%p end:
%p seq(a(n), n=0..20);
%Y Row n=3 of A225094.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Apr 27 2013
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