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A008862 Sum C(n,k), k=0..9. 14
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1023, 2036, 4017, 7814, 14913, 27824, 50643, 89846, 155382, 262144, 431910, 695860, 1097790, 1698160, 2579130, 3850756, 5658537, 8192524, 11698223, 16489546, 22964087, 31621024, 43081973, 58115146 (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 ten or fewer parts. - 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 (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).

FORMULA

a(n) = sum( binomial( n+1, 2k-1 ) for k=1..5 ), compare A008860.

G.f.: (1-8x+29x^2-62x^3+86x^4-80x^5+50x^6-20x^7+5x^8)/(1-x)^10 a(n)= (n^9 -27n^8 +366n^7 -2646n^6 +12873n^5 -31563n^4 +79064n^3 +34236n^2 +270576n +362880)/9!. - Geoffrey Critzer, Jan 24 2009

a(0)=1, a(1)=2, a(2)=4, a(3)=8, a(4)=16, a(5)=32, a(6)=64, a(7)=128, a(8)=256, a(9)=512, a(n)=10*a(n-1)-45*a(n-2)+120*a(n-3)-210*a(n-4)+252*a(n-5)- 210*a(n-6)+ 120*a(n-7)-45*a(n-8)+10*a(n-9)-a(n-10). - Harvey P. Dale, Mar 18 2012

EXAMPLE

a(10)=1023 because there are (2^10)-1 compositions of 11 into ten or fewer parts. - Geoffrey Critzer, Jan 24 2009

MATHEMATICA

Table[Sum[Binomial[n, k], {k, 0, 9}], {n, 0, 40}] (* or *) LinearRecurrence[ {10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {1, 2, 4, 8, 16, 32, 64, 128, 256, 512}, 40] (* Harvey P. Dale, Mar 18 2012 *)

PROG

(Haskell)

a008862 = sum . take 10 . a007318_row  -- Reinhard Zumkeller, Nov 24 2012

CROSSREFS

Cf. A008859, A008860, A008861, A008863, A006261, A000127.

Cf. A007318, A219531.

Sequence in context: A115213 A009714 A051535 * A145116 A172319 A234591

Adjacent sequences:  A008859 A008860 A008861 * A008863 A008864 A008865

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified October 22 06:02 EDT 2018. Contains 316432 sequences. (Running on oeis4.)