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A308113 Number of lattice paths from (0,0) to (n,n) that do not go above the diagonal x=y and consist of steps (h,v) with min(h,v) > 0 and gcd(h,v) = 1. 3
1, 1, 1, 2, 7, 22, 68, 205, 634, 2011, 6490, 21178, 69785, 231940, 776794, 2618951, 8881373, 30274185, 103673227, 356500914, 1230497234, 4261633997, 14805279769, 51580807121, 180173390369, 630864082719, 2213834486422, 7784823272163, 27427361186479 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..550

Wikipedia, Counting lattice paths

FORMULA

a(n) ~ c * d^n / n^(3/2), where d = 3.7137893481485186502229788321701955452444... and c = 0.47404607017890475336081188752626598456... - Vaclav Kotesovec, May 24 2019

MAPLE

b:= proc(x, y) option remember; `if`(y=0, 1, add(add(`if`(x+v

      >y+h or igcd(h, v)>1, 0, b(x-h, y-v)), v=1..y), h=1..x))

    end:

a:= n-> b(n$2):

seq(a(n), n=0..30);

CROSSREFS

Cf. A308087, A308114.

Sequence in context: A060816 A171847 A037552 * A291012 A294005 A292399

Adjacent sequences:  A308110 A308111 A308112 * A308114 A308115 A308116

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 13 2019

STATUS

approved

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Last modified September 17 11:15 EDT 2019. Contains 327129 sequences. (Running on oeis4.)