The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 Alois P. Heinz, Table of n, a(n) for n = 6..10000 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 Adjacent sequences: A002131 A002132 A002133 * A002135 A002136 A002137 KEYWORD nonn,easy AUTHOR N. J. A. Sloane EXTENSIONS Better description and more terms from Naohiro Nomoto, Jan 24 2002 More terms from Vladeta Jovovic, Nov 02 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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