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

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).

Mathematica

CoefficientList[Series[Times@@(1+x^Range[8]), {x, 0, 120}], x, 120] (* Harvey P. Dale, Jan 04 2025 *)

Prog

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

Crossrefs

Sequence in context: A111633 A273662 A396071 * A254667 A011879 A011878

Adjacent sequences: A034135 A034136 A034137 * A034139 A034140 A034141

Keyword

nonn

Author

N. J. A. Sloane

Status

approved