A034150 Number of partitions of n into distinct parts from [ 1, 20 ].

1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 27, 32, 38, 46, 54, 64, 75, 87, 101, 117, 135, 155, 178, 203, 231, 263, 297, 335, 378, 424, 475, 531, 591, 657, 729, 806, 889, 980, 1076, 1180, 1293, 1411, 1538, 1674

Offset

0,4

Comments

The number of different ways to run up a staircase with 20 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^20. - Mohammad K. Azarian, Aug 22 2010

References

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..48.

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

Formula

Expansion of (1+x)(1+x^2)(1+x^3)...(1+x^20).

Prog

(PARI) a(n) = polcoeff(prod(k=1, 20, 1 + x^k), n); \\ Michel Marcus, Mar 07 2015

Crossrefs

Sequence in context: A034148 A288000 A034149 * A347587 A288001 A034321

Adjacent sequences: A034147 A034148 A034149 * A034151 A034152 A034153

Keyword

nonn

Author

N. J. A. Sloane

Status

approved