A124841 Inverse binomial transform of A005614, the rabbit sequence: (1, 0, 1, 1, 0, ...).

1, -1, 2, -3, 3, 0, -10, 35, -90, 200, -400, 726, -1188, 1716, -2080, 1820, -312, -2704, 5408, 455, -39195, 170313, -523029, 1352078, -3114774, 6548074, -12668578, 22492886, -36020998, 49549110, -49549110, 0, 182029056, -670853984, 1809734560, -4242470755

Offset

0,3

Comments

As with every inverse binomial transform, the numbers are given by starting from the sequence (A005614) and reading the leftmost values of the array of repeated differences.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence)

Example

Given 1, 0, 1, 1, 0, ..., take finite difference rows:
1, 0, 1, 1, 0, ...
_-1, 1, 0, -1, ...
___ 2, -1, -1, ...
_____ -3, 0, ...
________ 3, ...
Left border becomes the sequence.

Mathematica

A005614 = SubstitutionSystem[{0 -> {1}, 1 -> {1, 0}}, {1, 0}, 7] // Last;
Table[Differences[A005614, n], {n, 0, 35}][[All, 1]] (* Jean-François Alcover, Feb 06 2020 *)

Crossrefs

Cf. A124842.

The following sequences are all essentially the same, in the sense that they are simple transformations of each other, with A000201 as the parent: A000201, A001030, A001468, A001950, A003622, A003842, A003849, A004641, A005614, A014675, A022342, A088462, A096270, A114986, A124841. - N. J. A. Sloane, Mar 11 2021

Sequence in context: A138003 A329232 A057682 * A085355 A103120 A021433

Adjacent sequences: A124838 A124839 A124840 * A124842 A124843 A124844

Keyword

sign

Author

Gary W. Adamson, Nov 10 2006

Extensions

Corrected and extended by R. J. Mathar, Nov 28 2011

Status

approved