A008640 Number of partitions of n into at most 11 parts.

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

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 A347577 A238869

Adjacent sequences: A008637 A008638 A008639 * A008641 A008642 A008643

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved