A225096 Number of lattice paths without interior points from {3}^n to {0}^n using steps that decrement one component by 1.

1, 0, 2, 384, 132000, 79716000, 78928416000, 120481708032000, 269702267433984000, 850271305403520000000, 3652393464869909760000000, 20798525597035736309760000000, 153427251286862484058423296000000, 1437639344607855309441929920512000000

Offset

0,3

Comments

An interior point p = (p_1, ..., p_n) has n>0 components with 0<p_i<3 for 1<=i<=n.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..100

Example

a(0) = 1: [()].
a(1) = 0, there is no path from (3) to (0) without interior points.
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)].

Maple

a:= proc(n) option remember; `if`(n<3, [1, 0, 2][n+1],
       (2*(3*n-1)*(3*n-2)*(7*n^2-9*n-4)*n*a(n-1)
       -3*n^2*(3*n-5)*(3*n-1)*(3*n-4)*(3*n-2)*(n-1)^2*a(n-2))/
       (8*(2*n+1)*(n-2)))
    end:
seq(a(n), n=0..20);

Crossrefs

Row n=3 of A225094.

Sequence in context: A329555 A171431 A280281 * A225111 A343698 A176937

Adjacent sequences: A225093 A225094 A225095 * A225097 A225098 A225099

Keyword

nonn

Author

Alois P. Heinz, Apr 27 2013

Status

approved