A051164 Sequence is defined by property that (a0,a1,a2,a3,...) = binomial transform of (a0,a0,a0,a1,a1,a1,a2,a2,a2,a3,a3,a3,...).

1, 2, 4, 9, 21, 48, 108, 243, 549, 1243, 2819, 6412, 14640, 33549, 77121, 177747, 410565, 949992, 2200978, 5103623, 11839783, 27471189, 63734823, 147831594, 342767586, 794413545, 1840338975, 4261443374, 9863627962, 22822212734, 52789053456, 122073285984

Offset: 0

Author

Jonas Wallgren

Keywords

• easy
• nonn
• eigen

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A051163, A051165, A051166.

Programs

Maple

a:= proc(n) option remember; add(`if`(k<3, 1,
      a(iquo(k, 3)))*binomial(n, k), k=0..n)
    end:
seq(a(n), n=0..40);  # Alois P. Heinz, Jul 08 2015

Mathematica

a[n_] := a[n] = Sum[If[k<3, 1, a[Quotient[k, 3]]]*Binomial[n, k], {k, 0, n}]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Feb 18 2017, after Alois P. Heinz *)

Extensions

More terms from Vladeta Jovovic, Jul 26 2002