The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A332829

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A332829

Number of compositions of n such that the difference between adjacent parts is at least two.
(history; published version)

#17 by Joerg Arndt at Wed Apr 13 07:40:21 EDT 2022

STATUS

reviewed

approved

#16 by Michel Marcus at Wed Apr 13 05:20:05 EDT 2022

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proposed

reviewed

#15 by Jean-François Alcover at Wed Apr 13 04:48:58 EDT 2022

STATUS

editing

proposed

#14 by Jean-François Alcover at Wed Apr 13 04:48:54 EDT 2022

MATHEMATICA

b[n_, i_] := b[n, i] = If[n == 0, 1, Sum[If[Abs[i - j] < 2, 0,

b[n - j, If[n < 2*j - 1, -1, j]]], {j, 1, n}]];

a[n_] := b[n, -1];

Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Apr 13 2022, after Alois P. Heinz *)

STATUS

approved

editing

#13 by Vaclav Kotesovec at Fri Feb 28 13:46:45 EST 2020

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editing

approved

#12 by Vaclav Kotesovec at Fri Feb 28 13:42:24 EST 2020

FORMULA

a(n) ~ c * d^n, where d = 1.55950091106966174000570854045613844480247532446123619115121795622156266..., c = 0.42021981384104890468461570042297109905705539874851026797544718780579866... - Vaclav Kotesovec, Feb 28 2020

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approved

editing

#11 by Alois P. Heinz at Tue Feb 25 22:35:32 EST 2020

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editing

approved

#10 by Alois P. Heinz at Tue Feb 25 22:35:25 EST 2020

EXAMPLE

a(5) = 4: 131, 14, 41, 5.

a(6) = 6: 141, 24, 42, 15, 51, 6.

a(8) = 15: 1313, 3131, 242, 314, 413, 152, 251, 35, 53, 161, 26, 62, 17, 71, 8.

STATUS

approved

editing

#9 by Alois P. Heinz at Tue Feb 25 22:25:35 EST 2020

STATUS

editing

approved

#8 by Alois P. Heinz at Tue Feb 25 22:25:01 EST 2020

LINKS

Alois P. Heinz, <a href="/A332829/b332829.txt">Table of n, a(n) for n = 0..1750</a>