A034137 Number of partitions of n into distinct parts from [ 1, 7 ].

1, 1, 1, 2, 2, 3, 4, 5, 5, 6, 7, 7, 8, 8, 8, 8, 8, 7, 7, 6, 5, 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, 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 7 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^7. - 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..80.

Formula

Expansion of (1+x)(1+x^2)(1+x^3)...(1+x^7).

Mathematica

PadRight[CoefficientList[Series[Times@@Table[1+x^n, {n, 7}], {x, 0, 100}], x], 100, 0] (* Harvey P. Dale, Jul 11 2014 *)

Crossrefs

Sequence in context: A236863 A242976 A218445 * A156351 A057561 A064726

Adjacent sequences: A034134 A034135 A034136 * A034138 A034139 A034140

Keyword

nonn

Author

N. J. A. Sloane

Status

approved