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A002134 Generalized divisor function. Number of partitions of n with exactly three part sizes.
(Formerly M1367 N0530)
9
1, 2, 5, 10, 15, 25, 37, 52, 67, 97, 117, 154, 184, 235, 277, 338, 385, 469, 531, 630, 698, 810, 910, 1038, 1144, 1295, 1425, 1577, 1741, 1938, 2089, 2301, 2505, 2700, 2970, 3189, 3444, 3703, 4004, 4242, 4617, 4882, 5244, 5558, 5999, 6221, 6755, 7050, 7576 (list; graph; refs; listen; history; text; internal format)
OFFSET
6,2
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
P. A. MacMahon, Divisors of numbers and their continuations in the theory of partitions, Proc. London Math. Soc., 19 (1919), 75-113; Coll. Papers II, pp. 303-341.
FORMULA
G.f.: Sum_{i>=1} Sum_{j=1..i-1} Sum_{k=1..j-1} x^(i+j+k)/((1-x^i)*(1-x^j)* (1-x^k)). - Geoffrey Critzer, Sep 13 2012
EXAMPLE
a(8) = 5 because we have 5+2+1, 4+3+1, 4+2+1+1, 3+2+2+1, 3+2+1+1+1.
MAPLE
# Using function P from A365676:
A002134 := n -> P(n, 3, n): seq(A002134(n), n = 6..54); # Peter Luschny, Sep 15 2023
MATHEMATICA
nn=40; sss=Sum[Sum[Sum[x^(i+j+k)/(1-x^i)/(1-x^j)/(1-x^k), {k, 1, j-1}], {j, 1, i-1}], {i, 1, nn}]; Drop[CoefficientList[Series[sss, {x, 0, nn}], x], 6] (* Geoffrey Critzer, Sep 13 2012 *)
CROSSREFS
A diagonal of A060177.
Column k=3 of A116608. - Alois P. Heinz, Nov 07 2012
Sequence in context: A099738 A064513 A117582 * A243971 A062472 A135061
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Better description and more terms from Naohiro Nomoto, Jan 24 2002
More terms from Vladeta Jovovic, Nov 02 2003
STATUS
approved

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Last modified June 16 19:52 EDT 2024. Contains 373432 sequences. (Running on oeis4.)