A034138 Number of partitions of n into distinct parts from [ 1, 8 ].

1, 1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 13, 13, 14, 13, 13, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,4

Comments

The number of different ways to run up a staircase with 8 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^8. - 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..74.

Formula

G.f.: (1+x)*(1+x^2)*(1+x^3)*...*(1+x^8).

Prog

(PARI) vector(100, n, polcoeff(prod(k=1, 8, (1+x^k)), n)) \\ Michel Marcus, Mar 07 2015

Crossrefs

Sequence in context: A289188 A111633 A273662 * A254667 A011879 A011878

Adjacent sequences: A034135 A034136 A034137 * A034139 A034140 A034141

Keyword

nonn

Author

N. J. A. Sloane

Status

approved