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Search: id:A014968
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| A014968 |
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Expansion of (1/theta_4 - 1)/2. |
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1
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| 0, 1, 2, 4, 7, 12, 20, 32, 50, 77, 116, 172, 252, 364, 520, 736, 1031, 1432, 1974, 2700, 3668, 4952, 6644, 8864, 11764, 15533, 20412, 26704, 34784, 45124, 58312, 75072, 96306, 123128, 156904, 199320, 252443
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Let p(n) = the number of partitions of n, p(i,n) = the number of parts of the i-th partition of n, d(i,n) = the number of different parts in the i-th partition of n. Then a(n) = Sum_{i=1}^{p(n)} Sum_{j=1}^d(i,n) binomial(d(i,n)-1,j-1). - Thomas Wieder (wieder.thomas(AT)t-online.de), May 08 2005
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REFERENCES
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J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 103.
A. Fink, R. K. Guy and M. Krusemeyer, Partitions with parts occurring at most thrice, in preparation.
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MAPLE
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A014968 := proc(n::integer) local a, i, j, prttn, prttnlst, ZahlTeile, ZahlVerschiedenerTeile; #with(combinat); a := 0; prttnlst:=partition(n); for i from 1 to nops(prttnlst) do prttn := prttnlst[i]; ZahlTeile := nops(prttn); ZahlVerschiedenerTeile:=nops(convert(prttn, multiset)); for j from 1 to ZahlVerschiedenerTeile do a := a + binomial(ZahlVerschiedenerTeile-1, j-1); od; od; print("n, a(n): ", n, a); end proc; (Wieder)
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CROSSREFS
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Equals (A015128(n)-1)/2.
Sequence in context: A132218 A101230 A128129 this_sequence A126348 A006731 A000071
Adjacent sequences: A014965 A014966 A014967 this_sequence A014969 A014970 A014971
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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