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A168445 Number of compositions a(1),...,a(k) of n, for some k, such that a(i+1) <= a(i) + 1 for 1 <= i < k and a(1) <= a(k) + 1. 3
1, 2, 4, 6, 11, 18, 31, 52, 91, 155, 268, 464, 802, 1390, 2411, 4178, 7249, 12578, 21823, 37870, 65724, 114061, 197960, 343578, 596317, 1034983, 1796359, 3117837, 5411478, 9392460, 16302081, 28294850, 49110242, 85238716, 147945552, 256783448, 445689300 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

S. R. Finch, Mathematical Constants, Cambridge, 2003, p. 381.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..400

FORMULA

a(n) ~ c * d^n, where d=1.7356628245303474256582607497196685302546528472903927546099..., c=0.6149126319329581124890112676009720339906790088212712130894... - Vaclav Kotesovec, May 01 2014

Constant d = 1 / 0.576148769142756... (see A005169, constant x). - Vaclav Kotesovec, Jun 04 2014

MAPLE

b:= proc(n, r, f) option remember; `if` (n=0, `if` (f-1<=r, 1, 0), add (b(n-i, i, f), i=1..min (r+1, n))) end: a:= n-> add (b(n-i, i, i), i=1..n): seq (a(n), n=1..40); # Alois P. Heinz, Dec 15 2009

CROSSREFS

Cf. A003116, A005169.

Sequence in context: A026658 A138688 A131298 * A185192 A007053 A005684

Adjacent sequences:  A168442 A168443 A168444 * A168446 A168447 A168448

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Nov 25 2009

EXTENSIONS

More terms from Alois P. Heinz, Dec 15 2009

STATUS

approved

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Last modified May 26 22:57 EDT 2019. Contains 323597 sequences. (Running on oeis4.)