A051166 Sequence is defined by property that binomial transform of (a0,a1,a2,a3,...) = (a0,a0,a0,a1,a1,a1,a2,a2,a2,a3,a3,a3,...).

1, 0, 0, -1, 3, -6, 10, -15, 21, -29, 45, -90, 224, -609, 1677, -4559, 12135, -31542, 80086, -199035, 485469, -1165105, 2757369, -6446778, 14913052, -34175805, 77672325, -175228740, 392711166, -874901088, 1938704130, -4275110880, 9385473510, -20521355211, 44704157499, -97055415324

Offset: 0

Author

Jonas Wallgren

Keywords

• easy
• sign
• eigen

Links

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

Crossrefs

Cf. A051163, A051164, A051165.

Programs

Maple

a:= proc(n) option remember; add(`if`(k<3, 1,
      a(iquo(k, 3)))*(-1)^(n-k)*binomial(n, k), k=0..n)
    end:
seq(a(n), n=0..45);  # Alois P. Heinz, Jul 08 2015

Mathematica

a[n_] := a[n] = Sum[If[k<3, 1, a[Quotient[k, 3]]]*(-1)^(n-k)*Binomial[n, k], {k, 0, n}];
Table[a[n], {n, 0, 45}] (* Jean-François Alcover, Apr 04 2017, after Alois P. Heinz *)

Extensions

More terms from Vladeta Jovovic, Jul 26 2002