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Search: id:A026824
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| A026824 |
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Number of partitions of n into distinct parts, the least being 3. |
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+0
3
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| 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 6, 6, 8, 9, 11, 12, 15, 17, 20, 23, 27, 31, 36, 41, 47, 55, 62, 71, 81, 93, 105, 120, 135, 154, 174, 197, 221, 251, 281, 317, 356, 400, 447, 502, 561, 628, 701, 782, 871, 972, 1081, 1202, 1336, 1483, 1645, 1825, 2021, 2237, 2476
(list; graph; listen)
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OFFSET
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0,13
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COMMENT
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Also number of partitions of n such that if k is the largest part, then k occurs exactly 3 times and each of the numbers 1,2,...,k-1 occurs at least once (these are the conjugates of the partitions described in the definition). Example: a(14)=3 because we have [3,3,3,2,2,1],[3,3,3,2,1,1,1], and [2,2,2,1,1,1,1,1,1,1,1]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 17 2006
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FORMULA
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G.f.=(x^3)product(1+x^j, j=4..infinity). G.f.=sum(x^(k(k+5)/2)/product(1-x^j, j=1..k-1), k=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 17 2006
a(n)=A025149(n-3), n>3. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 31 2008
G.f.: x^3*product_{j=4..infinity} (1+x^j). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 31 2008
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EXAMPLE
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a(14)=3 because we have [11,3],[7,4,3], and [6,5,3].
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MAPLE
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g:=x^3*product(1+x^j, j=4..80): gser:=series(g, x=0, 70): seq(coeff(gser, x, n), n=1..59); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 17 2006
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CROSSREFS
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Adjacent sequences: A026821 A026822 A026823 this_sequence A026825 A026826 A026827
Sequence in context: A029026 A003106 A025149 this_sequence A026799 A027190 A036824
Cf. A025147.
Cf. A025147.
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 17 2006
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