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A263316 Number of lattice paths from (0,0) to (n,n) which do not go above the diagonal x=y using steps (1,k), (k,1) with k>=2. 4
1, 0, 0, 1, 1, 3, 7, 16, 40, 98, 246, 624, 1596, 4120, 10708, 28009, 73673, 194743, 517067, 1378365, 3687665, 9898417, 26649117, 71943947, 194717215, 528236599, 1436122339, 3912244667, 10677558423, 29192753795, 79944089343, 219261036592, 602226736360 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

EXAMPLE

a(0) = 1: [(0,0)].

a(3) = 1: [(0,0),(2,1),(3,3)].

a(4) = 1: [(0,0),(3,1),(4,4)].

a(5) = 3: [(0,0),(3,1),(4,3),(5,5)], [(0,0),(2,1),(4,2),(5,5)], [(0,0),(4,1),(5,5)].

a(6) = 7: [(0,0),(2,1),(3,3),(5,4),(6,6)], [(0,0),(2,1),(4,2),(5,4),(6,6)], [(0,0),(4,1),(5,4),(6,6)], [(0,0),(4,1),(5,3),(6,6)], [(0,0),(3,1),(5,2),(6,6)], [(0,0),(2,1),(5,2),(6,6)], [(0,0),(5,1),(6,6)].

MAPLE

a:= proc(n) option remember; `if`(n<5, [1, 0$2, 1$2][n+1],

      ((n-3)*a(n-1) +(5*n-5)*a(n-2) +(3*n-3)*a(n-3)

       -(4*n-20)*a(n-4) -(4*n-16)*a(n-5))/(n+1))

    end:

seq(a(n), n=0..40);

CROSSREFS

Cf. A014137, A082582, A168592, A218321.

Sequence in context: A103439 A147321 A103030 * A001698 A261236 A029761

Adjacent sequences:  A263313 A263314 A263315 * A263317 A263318 A263319

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 14 2015

STATUS

approved

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Last modified October 21 08:27 EDT 2018. Contains 316405 sequences. (Running on oeis4.)