A085811 Number of partitions of n including 3, but not 1.

0, 0, 1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21, 24, 34, 41, 55, 66, 88, 105, 137, 165, 210, 253, 320, 383, 478, 574, 708, 847, 1039, 1238, 1507, 1794, 2167, 2573, 3094, 3660, 4378, 5170, 6153, 7245, 8591, 10087, 11914, 13959, 16424, 19196, 22519, 26252, 30701

Offset

1,7

Comments

Essentially the same as A002865.

Links

Andrew van den Hoeven, Table of n, a(n) for n = 1..10000

Formula

A002865(n) = a(n+3). - James Sellers, Dec 06 2005

G.f.: x^3*(1-x)/Product_{n>=1} (1-x^n). - Joerg Arndt, Feb 03 2012

Example

a(3): 3
a(5): 2+3
a(6): 3+3
a(7): 2+2+3, 3+4
a(8): 2+3+3, 3+5
a(9): 2+3+4, 2+2+2+3, 3+3+3, 3+6
a(10): 2+3+5, 2+2+3+3, 3+7, 3+3+4
a(11): 2+2+3+4, 2+3+6, 2+2+2+2+3, 2+3+3+3, 3+4+4, 3+8, 3+3+5,
a(12): 2+2+2+3+3, 2+3+3+4, 2+3+7, 2+2+3+5, 3+9, 3+3+6, 3+4+5, 3+3+3+3
a(13): 2+2+2+2+2+3, 2+2+2+3+4, 2+2+3+6, 2+2+3+3+3, 2+3+4+4, 2+3+3+5,
2+3+8, 3+10, 3+3+7, 3+4+6, 3+5+5, 3+3+3+4

Mathematica

CoefficientList[x^2*(1-x)/QPochhammer[x] + O[x]^60, x] (* Jean-François Alcover, Jan 22 2016, after Joerg Arndt *)

Prog

(PARI) my(x='x+O('x^66)); Vec((x^3*(1-x)/eta(x)))  /* Joerg Arndt, Feb 03 2012 */

Crossrefs

Cf. A008483. Essentially the same as A002865.

Sequence in context: A240019 A036000 A002865 * A187219 A317785 A014810

Adjacent sequences: A085808 A085809 A085810 * A085812 A085813 A085814

Keyword

nonn

Author

Jon Perry, Jul 25 2003

Extensions

Edited, corrected and extended by Robert G. Wilson v

Typo in formula corrected by Andrew van den Hoeven, Nov 20 2014

Status

approved