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A124841 Inverse binomial transform of A005614, the rabbit sequence: (1, 0, 1, 1, 0, ...). 16

%I

%S 1,-1,2,-3,3,0,-10,35,-90,200,-400,726,-1188,1716,-2080,1820,-312,

%T -2704,5408,455,-39195,170313,-523029,1352078,-3114774,6548074,

%U -12668578,22492886,-36020998,49549110,-49549110,0,182029056,-670853984,1809734560,-4242470755

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

%C 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.

%H Alois P. Heinz, <a href="/A124841/b124841.txt">Table of n, a(n) for n = 0..1000</a>

%H N. J. A. Sloane, <a href="/A115004/a115004.txt">Families of Essentially Identical Sequences</a>, Mar 24 2021 (Includes this sequence)

%e Given 1, 0, 1, 1, 0, ..., take finite difference rows:

%e 1, 0, 1, 1, 0, ...

%e _-1, 1, 0, -1, ...

%e ___ 2, -1, -1, ...

%e _____ -3, 0, ...

%e ________ 3, ...

%e Left border becomes the sequence.

%t A005614 = SubstitutionSystem[{0 -> {1}, 1 -> {1, 0}}, {1, 0}, 7] // Last;

%t Table[Differences[A005614, n], {n, 0, 35}][[All, 1]] (* _Jean-Fran├žois Alcover_, Feb 06 2020 *)

%Y Cf. A124842.

%Y 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

%K sign

%O 0,3

%A _Gary W. Adamson_, Nov 10 2006

%E Corrected and extended by _R. J. Mathar_, Nov 28 2011

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Last modified July 27 15:06 EDT 2021. Contains 346307 sequences. (Running on oeis4.)