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A034142
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Number of partitions of n into distinct parts from [ 1, 12 ].
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0
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1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 27, 31, 36, 40, 45, 51, 56, 61, 67, 72, 78, 84, 89, 94, 100, 104, 108, 113, 115, 118, 121, 122, 123, 124, 123, 122, 121, 118, 115, 113, 108, 104, 100, 94, 89, 84, 78
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| The number of different ways to run up a staircase with 12 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^12.
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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, 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).
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FORMULA
| Expansion of (1+x)(1+x^2)(1+x^3)...(1+x^12).
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MATHEMATICA
| CoefficientList[Series[Times@@Table[(1+x^n), {n, 12}], {x, 0, 60}], x] (* From Harvey P. Dale, Jul 19 2011 *)
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CROSSREFS
| Sequence in context: A114097 A174246 A083847 * A008675 A027581 A058706
Adjacent sequences: A034139 A034140 A034141 * A034143 A034144 A034145
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Added a comment and 2 references by Mohammad K. Azarian (azarian(AT)evansville.edu), Aug 22 2010
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