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A308114 Total number of nodes summed over all 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, 2, 3, 7, 26, 92, 314, 1055, 3589, 12410, 43356, 152336, 537721, 1906063, 6781737, 24206994, 86644157, 310871212, 1117741815, 4026430097, 14528792287, 52504325068, 189999731589, 688411569408, 2497081766875, 9067028323162, 32953990726244, 119875216666167 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Wikipedia, Counting lattice paths

FORMULA

a(n) ~ c * d^n / sqrt(n), where d = 3.7137893481485186502229788321701955452444... and c = 0.243302622746026118665161170169985306... - Vaclav Kotesovec, May 24 2019

MAPLE

b:= proc(x, y) option remember; `if`(y=0, [1$2], (p-> p+

      [0, p[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)[2]:

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

CROSSREFS

Cf. A308112, A308113.

Sequence in context: A063852 A301519 A274692 * A092983 A089708 A107881

Adjacent sequences:  A308111 A308112 A308113 * A308116 A308117 A308118

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 13 2019

STATUS

approved

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Last modified June 25 07:53 EDT 2019. Contains 324347 sequences. (Running on oeis4.)