A034149 Number of partitions of n into distinct parts from [ 1, 19 ].

1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 27, 32, 38, 46, 54, 63, 74, 86, 99, 115, 132, 151, 173, 197, 223, 253, 285, 320, 360, 402, 448, 499, 553, 611, 675, 743, 815, 894, 977, 1065, 1161, 1260, 1365, 1477

Offset

0,4

Comments

The number of different ways to run up a staircase with 19 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^19. - 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..48.

Formula

Expansion of (1+x)(1+x^2)(1+x^3)...(1+x^19).

Crossrefs

Sequence in context: A034147 A034148 A288000 * A034150 A347587 A288001

Adjacent sequences: A034146 A034147 A034148 * A034150 A034151 A034152

Keyword

nonn

Author

N. J. A. Sloane

Status

approved