A210486 Number of paths starting at {3}^n to a border position where one component equals 0 using steps that decrement one component by 1.

0, 1, 20, 543, 22096, 1304045, 106478916, 11545342795, 1608000044288, 280061940550041, 59677171216017940, 15278632095285640631, 4628964787172536267920, 1638318264614752659427333, 669895681115518466689138436, 313418973409285344224352078435

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..237

Formula

a(n) ~ sqrt(Pi) * 2^(n+1) * n^(2*n+3/2) / exp(2*n-1). - Vaclav Kotesovec, Sep 02 2014

Example

a(1) = 1: [3, 2, 1, 0].
a(2) = 20: [33, 23, 13, 03], [33, 23, 13, 12, 02], [33, 23, 13, 12, 11, 01], [33, 23, 13, 12, 11, 10], [33, 23, 22, 12, 02], [33, 23, 22, 12, 11, 01], [33, 23, 22, 12, 11, 10], [33, 23, 22, 21, 11, 01], [33, 23, 22, 21, 11, 10], [33, 23, 22, 21, 20], [33, 32, 22, 12, 02], [33, 32, 22, 12, 11, 01], [33, 32, 22, 12, 11, 10], [33, 32, 22, 21, 11, 01], [33, 32, 22, 21, 11, 10], [33, 32, 22, 21, 20], [33, 32, 31, 21, 11, 01], [33, 32, 31, 21, 11, 10], [33, 32, 31, 21, 20], [33, 32, 31, 30].

Maple

a:= proc(n) option remember; `if`(n<3, [0, 1, 20][n+1],
      ((n-1)*(n-2)*(n+1)*a(n-3) -(n-1)*(3*n^2-2*n-4)*a(n-2)
      +(2*n+1)*(n^2-n+2)*a(n-1)) / (n-1))
    end:
seq(a(n), n=0..20);  # Alois P. Heinz, Jan 23 2013

Mathematica

a[n_] := a[n] = If[n<3, {0, 1, 20}[[n+1]], ((n-1)*(n-2)*(n+1)*a[n-3] - (n-1)*(3*n^2 - 2*n - 4)*a[n-2] + (2*n+1)*(n^2 - n + 2)*a[n-1]) / (n-1)];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Mar 29 2017, after Alois P. Heinz *)

Crossrefs

Row n=3 of A210472.

Sequence in context: A337352 A180882 A202920 * A047682 A231249 A012568

Adjacent sequences: A210483 A210484 A210485 * A210487 A210488 A210489

Keyword

nonn,walk

Author

Alois P. Heinz, Jan 23 2013

Status

approved