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A317782 Number of 2n-step paths from (0,0) to (0,n) that stay in the first quadrant (but may touch the axes) consisting of steps (1,0), (0,1), (0,-1) and (-1,1). 3

%I

%S 1,1,5,51,474,4329,43406,469565,5228459,59259957,686003702,8097484169,

%T 97005128492,1175916181703,14404685872773,178105648065109,

%U 2220134252592683,27872257776993240,352143374331177766,4474477933645201621,57147423819800882972

%N Number of 2n-step paths from (0,0) to (0,n) that stay in the first quadrant (but may touch the axes) consisting of steps (1,0), (0,1), (0,-1) and (-1,1).

%H Alois P. Heinz, <a href="/A317782/b317782.txt">Table of n, a(n) for n = 0..500</a>

%F a(n) = A199915(2n,n).

%F a(n) ~ c * d^n / n^2, where d = 14.0982628380912972017512943055944... and c = 0.25546328221900708410379626465... - _Vaclav Kotesovec_, Mar 13 2019

%e a(2) = 5: [(0,1),(0,-1),(0,1),(0,1)], [(0,1),(0,1),(0,-1),(0,1)], [(0,1),(0,1),(0,1),(0,-1)], [(1,0),(-1,1),(1,0),(-1,1)], [(1,0),(1,0),(-1,1),(-1,1)].

%p b:= proc(n, x, y) option remember; `if`(min(args, n-x-y)<0, 0, `if`(n=0, 1,

%p add(b(n-1, x-d[1], y-d[2]), d=[[1, 0], [0, 1], [0, -1], [-1, 1]])))

%p end:

%p a:= n-> b(2*n, 0, n):

%p seq(a(n), n=0..25);

%Y Cf. A199915, A306813.

%K nonn,walk

%O 0,3

%A _Alois P. Heinz_, Sep 24 2018

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Last modified January 19 21:47 EST 2020. Contains 331066 sequences. (Running on oeis4.)