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A383477

Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) is the number of lattice paths from (0,0) to (n,k) using steps (1,0),(2,0),(3,0),(0,1).

1, 1, 1, 1, 2, 2, 1, 3, 5, 4, 1, 4, 9, 12, 7, 1, 5, 14, 25, 26, 13, 1, 6, 20, 44, 63, 56, 24, 1, 7, 27, 70, 125, 153, 118, 44, 1, 8, 35, 104, 220, 336, 359, 244, 81, 1, 9, 44, 147, 357, 646, 864, 819, 499, 149, 1, 10, 54, 200, 546, 1134, 1800, 2144, 1830, 1010, 274

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OFFSET

0,5

LINKS

Table of n, a(n) for n=0..65.

FORMULA

A(n,k) = A(n-1,k) + A(n-2,k) + A(n-3,k) + A(n,k-1).

G.f.: 1 / (1 - x - x^2 - x^3 - y).

G.f. of column k: 1 / (1 - x - x^2 - x^3)^(k+1).

EXAMPLE

Square array A(n,k) begins:

1, 1, 1, 1, 1, 1, 1, ...