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A079501
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Number of compositions of the integer n with strictly smallest part in the first position.
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5
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1, 1, 2, 2, 4, 5, 8, 12, 19, 28, 45, 70, 110, 173, 275, 436, 695, 1107, 1769, 2831, 4537, 7276, 11683, 18774, 30194, 48592, 78247, 126062, 203192, 327645, 528518, 852815, 1376491, 2222294, 3588628, 5796196, 9363458, 15128631, 24447014, 39510108
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Also number of compositions of n such that the first part is divisible by the number of parts . [From Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 02 2009]
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REFERENCES
| Arnold Knopfmacher and Neville Robbins, Compositions with parts constrained by the leading summand, Ars Combin. 76 (2005), 287-295.
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FORMULA
| G.f.: sum (1-z)z^k/(1-z-z^(k+1)); k=1..inf
Also sum z^(2*k-1)/((1-z^k)*(1-z)^(k-1)); k=1..inf, cf. A105039. - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 05 2005
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EXAMPLE
| For example for n=8 we count 2+3+3 but not 2+4+2 and not 2+1+5
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CROSSREFS
| Cf. A168655, A168656, A168657. [From Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 02 2009]
Sequence in context: A078465 A094992 A172128 * A093335 A093333 A116085
Adjacent sequences: A079498 A079499 A079500 * A079502 A079503 A079504
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KEYWORD
| nonn
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AUTHOR
| Arnold Knopfmacher (arnoldk(AT)cam.wits.ac.za), Jan 21 2003
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EXTENSIONS
| More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 21 2003
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