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A008640 Number of partitions of n into at most 11 parts. 3
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 76, 99, 131, 169, 219, 278, 355, 445, 560, 695, 863, 1060, 1303, 1586, 1930, 2331, 2812, 3370, 4035, 4802, 5708, 6751, 7972, 9373, 11004, 12866, 15021, 17475, 20298, 23501, 27169, 31316, 36043, 41373, 47420, 54218, 61903, 70515, 80215, 91058, 103226, 116792, 131970, 148847 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For n>10: also number of partitions of n into parts <= 11: a(n)=A026820(n,11). [Reinhard Zumkeller, Jan 21 2010]

REFERENCES

A. Cayley, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 10, p. 415.

H. Gupta et al., Tables of Partitions. Royal Society Mathematical Tables, Vol. 4, Cambridge Univ. Press, 1958, p. 2.

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 360

Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, -1, -1, -1, -2, -1, -1, 0, -1, 2, 2, 2, 2, 1, 1, 0, -1, -1, -2, -2, -2, -2, 1, 0, 1, 1, 2, 1, 1, 1, 0, 0, -1, -2, -1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, -1, -1, 1).

FORMULA

a(n) = a(n-1) + a(n-2) - a(n-5) - a(n-7) + a(n-14) + 2*a(n-15) + a(n-16) - a(n-19) - a(n-20) - a(n-21) - 2*a(n-22) - a(n-23) - a(n-24) - a(n-26) + 2*a(n-27) + 2*a(n-28) + 2*a(n-29) + 2*a(n-30) + a(n-31) + a(n-32) - a(n-34) - a(n-35) - 2*a(n-36) - 2*a(n-37) - 2*a(n-38) - 2*a(n-39) + a(n-40) + a(n-42) + a(n-43) + 2*a(n-44) + a(n-45) + a(n-46) + a(n-47) - a(n-50) - 2*a(n-51) - a(n-52) + a(n-59) + a(n-61) - a(n-64) - a(n-65) + a(n-66). - David Neil McGrath, Jul 27 2015

G.f.: 1 / prod(k=1..11, 1 - x^k ). - Joerg Arndt, Aug 04 2015

MAPLE

1/(1-x)/(1-x^2)/(1-x^3)/(1-x^4)/(1-x^5)/(1-x^6)/(1-x^7)/(1-x^8)/(1-x^9)/(1-x^10)/(1-x^11)

with(combstruct):ZL12:=[S, {S=Set(Cycle(Z, card<12))}, unlabeled]: seq(count(ZL12, size=n), n=0..44); # Zerinvary Lajos, Sep 24 2007

B:=[S, {S = Set(Sequence(Z, 1 <= card), card <=11)}, unlabelled]: seq(combstruct[count](B, size=n), n=0..44); # Zerinvary Lajos, Mar 21 2009

MATHEMATICA

CoefficientList[ Series[ 1/ Product[ 1 - x^n, {n, 1, 11} ], {x, 0, 60} ], x ]

CROSSREFS

Differs from A008634 at 55th term.

a(n) = A008284(n+11, 11), n >= 0.

Sequence in context: A328545 A192061 A218511 * A008634 A238869 A326333

Adjacent sequences:  A008637 A008638 A008639 * A008641 A008642 A008643

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 13 06:02 EDT 2021. Contains 342935 sequences. (Running on oeis4.)