A034142 Number of partitions of n into distinct parts from [ 1, 12 ].

1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 27, 31, 36, 40, 45, 51, 56, 61, 67, 72, 78, 84, 89, 94, 100, 104, 108, 113, 115, 118, 121, 122, 123, 124, 123, 122, 121, 118, 115, 113, 108, 104, 100, 94, 89, 84, 78

Offset

0,4

Comments

The number of different ways to run up a staircase with 12 steps, taking steps of odd sizes (or taking steps of distinct sizes), where the order is not relevant and there is no other restriction on the number or the size of each step taken is the coefficient of x^12. - Mohammad K. Azarian, Aug 22 2010

References

Mohammad K. Azarian, A Generalization of the Climbing Stairs Problem II, Missouri Journal of Mathematical Sciences, Vol. 16, No. 1, Winter 2004, pp. 12-17. Zentralblatt MATH, Zbl 1071.05501. - Mohammad K. Azarian, Aug 22 2010

Mohammad K. Azarian, A Generalization of the Climbing Stairs Problem, Mathematics and Computer Education, Vol. 31, No. 1, pp. 24-28, Winter 1997. MathEduc Database (Zentralblatt MATH, 1997c.01891). - Mohammad K. Azarian, Aug 22 2010

Links

Table of n, a(n) for n=0..52.

Formula

Expansion of (1+x)(1+x^2)(1+x^3)...(1+x^12).

Mathematica

CoefficientList[Series[Times@@Table[(1+x^n), {n, 12}], {x, 0, 60}], x] (* Harvey P. Dale, Jul 19 2011 *)

Crossrefs

Sequence in context: A325855 A174246 A083847 * A008675 A027581 A058706

Adjacent sequences: A034139 A034140 A034141 * A034143 A034144 A034145

Keyword

nonn

Author

N. J. A. Sloane

Status

approved