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A008861 Sum C(n,k), k=0..8. 14
1, 2, 4, 8, 16, 32, 64, 128, 256, 511, 1013, 1981, 3797, 7099, 12911, 22819, 39203, 65536, 106762, 169766, 263950, 401930, 600370, 880970, 1271626, 1807781, 2533987, 3505699, 4791323, 6474541, 8656937, 11460949, 15033173, 19548046 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n)is the number of compositions (ordered partitions) of n+1 into nine or fewer parts. [From Geoffrey Critzer, Jan 24 2009]

REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 72, Problem 2.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

FORMULA

a(n)=sum(binomial(n+1, 2k), k=0..4), compare A008859.

G.f.: (1-7x+22x^2-40x^3+46x^4-34x^5+16x^6-4x^7+x^8)/(1-x)^9 a(n)= (n^8-20n^7+210n^6-1064n^5+3969n^4-4340n^3+15980n^2+25584n+40320)/8! [From Geoffrey Critzer, Jan 24 2009]

EXAMPLE

a(9)=511 because all but one (namely 1+1+1+...+1=10) of the 2^9 compositions of 10 are in nine or fewer parts. [From Geoffrey Critzer, Jan 24 2009]

PROG

(Haskell)

a008861 = sum . take 9 . a007318_row -- Reinhard Zumkeller, Nov 24 2012

CROSSREFS

Cf. A008859, A008860, A008862, A008863, A006261, A000127.

Cf. A007318, A219531.

Sequence in context: A271481 A208849 A054046 * A145115 A172318 A234590

Adjacent sequences:  A008858 A008859 A008860 * A008862 A008863 A008864

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, R. K. Guy

STATUS

approved

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Last modified October 17 06:27 EDT 2018. Contains 316276 sequences. (Running on oeis4.)