A034144 Number of partitions of n into distinct parts from [ 1, 14 ].

1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 26, 30, 35, 41, 47, 54, 62, 70, 79, 89, 99, 110, 122, 134, 146, 160, 173, 187, 202, 216, 231, 246, 260, 274, 289, 302, 315, 328, 339, 350, 361, 369, 377, 384, 389, 393

Offset

0,4

Comments

The number of different ways to run up a staircase with 14 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^14. - 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..50.

Formula

Expansion of (1+x)(1+x^2)(1+x^3)...(1+x^14).

Mathematica

CoefficientList[Series[Times@@Table[1+x^n, {n, 14}], {x, 0, 50}], x] (* Harvey P. Dale, Apr 07 2015 *)

Crossrefs

Sequence in context: A058706 A034143 A309999 * A347586 A287997 A352165

Adjacent sequences: A034141 A034142 A034143 * A034145 A034146 A034147

Keyword

nonn

Author

N. J. A. Sloane

Status

approved