

A317782


Number of 2nstep 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



1, 1, 5, 51, 474, 4329, 43406, 469565, 5228459, 59259957, 686003702, 8097484169, 97005128492, 1175916181703, 14404685872773, 178105648065109, 2220134252592683, 27872257776993240, 352143374331177766, 4474477933645201621, 57147423819800882972
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OFFSET

0,3


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500


FORMULA

a(n) = A199915(2n,n).
a(n) ~ c * d^n / n^2, where d = 14.0982628380912972017512943055944... and c = 0.25546328221900708410379626465...  Vaclav Kotesovec, Mar 13 2019


EXAMPLE

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)].


MAPLE

b:= proc(n, x, y) option remember; `if`(min(args, nxy)<0, 0, `if`(n=0, 1,
add(b(n1, xd[1], yd[2]), d=[[1, 0], [0, 1], [0, 1], [1, 1]])))
end:
a:= n> b(2*n, 0, n):
seq(a(n), n=0..25);


CROSSREFS

Cf. A199915, A306813.
Sequence in context: A208997 A041043 A145641 * A195211 A106415 A212819
Adjacent sequences: A317779 A317780 A317781 * A317783 A317784 A317785


KEYWORD

nonn,walk


AUTHOR

Alois P. Heinz, Sep 24 2018


STATUS

approved



