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A035363
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Number of partitions of n into even parts.
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11
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1, 0, 1, 0, 2, 0, 3, 0, 5, 0, 7, 0, 11, 0, 15, 0, 22, 0, 30, 0, 42, 0, 56, 0, 77, 0, 101, 0, 135, 0, 176, 0, 231, 0, 297, 0, 385, 0, 490, 0, 627, 0, 792, 0, 1002, 0, 1255, 0, 1575, 0, 1958, 0, 2436, 0, 3010, 0, 3718, 0, 4565, 0, 5604, 0, 6842, 0, 8349, 0, 10143, 0, 12310, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Convolved with A036469 = A000070 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 09 2009]
Note that these partitions are located in the head of the outer shell of the partitions of n (see A135010). [From Omar E. Pol (info(AT)polprimos.com), Nov 20 2009]
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REFERENCES
| 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, 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.
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FORMULA
| G.f.: prod(1/(1-x^k), k even)
Convolution with the number of partitions into distinct parts (A000009, which is also number of partitions into odd parts) gives the number of partitions (A000041). - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 06 2006
If n is even then a(n)=A000041(n/2) otherwise a(n)=0. [From Omar E. Pol (info(AT)polprimos.com), Nov 20 2009]
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MAPLE
| ZL:= [S, {C = Cycle(B), S = Set(C), E = Set(B), B = Prod(Z, Z)}, unlabelled]: seq(combstruct[count](ZL, size=n), n=0..69); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 26 2008
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CROSSREFS
| Subsequence a(2n) is simply the partition numbers A000041.
First column (m=0) of triangle A103919.
A036469, A000070 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 09 2009]
Cf. A135010, A138121. [From Omar E. Pol (info(AT)polprimos.com), Nov 20 2009]
Sequence in context: A008820 A066682 A049641 * A079977 A008799 A011013
Adjacent sequences: A035360 A035361 A035362 * A035364 A035365 A035366
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KEYWORD
| nonn,easy
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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