A034140 Number of partitions of n into distinct parts from [ 1,2,3,...,10 ].

1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 27, 29, 31, 33, 35, 36, 38, 39, 39, 40, 40, 39, 39, 38, 36, 35, 33, 31, 29, 27, 24, 22, 20, 17, 15, 13, 11, 10, 8, 6, 5, 4, 3, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,4

Comments

The number of different ways to run up a staircase with 10 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^10. - 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..63.

Formula

Expansion of (1+x)*(1+x^2)*(1+x^3)*...*(1+x^10).

Mathematica

Join[CoefficientList[Series[Times@@Table[1+x^n, {n, 10}], {x, 0, 64}], x], Table[0, {8}]] (* Harvey P. Dale, Jun 17 2011 *)

Crossrefs

Sequence in context: A325877 A100928 A240671 * A109950 A008674 A067596

Adjacent sequences: A034137 A034138 A034139 * A034141 A034142 A034143

Keyword

nonn

Author

N. J. A. Sloane

Status

approved