A034148 Number of partitions of n into distinct parts from [ 1, 18 ].

1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 27, 32, 38, 46, 53, 62, 73, 84, 97, 112, 128, 146, 167, 189, 213, 241, 270, 302, 338, 375, 416, 461, 507, 558, 613, 670, 731, 797, 865, 937, 1015, 1093, 1176, 1264

Offset

0,4

Comments

The number of different ways to run up a staircase with 18 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^18. - 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, 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).

Links

Table of n, a(n) for n=0..48.

Formula

Expansion of (1+x)(1+x^2)(1+x^3)...(1+x^18).

Crossrefs

Sequence in context: A034146 A287998 A034147 * A288000 A034149 A034150

Adjacent sequences: A034145 A034146 A034147 * A034149 A034150 A034151

Keyword

nonn

Author

N. J. A. Sloane

Status

approved