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
Keywords
Examples
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.
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)
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
Programs
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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 *)
Extensions
Corrected and extended by R. J. Mathar, Nov 28 2011
Comments