OFFSET
0,2
COMMENTS
From R. J. Mathar, Oct 26 2011: (Start)
Row T(3,k) in the array of triangular partitions of k:
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...
1,2,3,5,7,9,12,15,18,22,26,30,35,40,45,51,57,63,70,...
1,3,6,12,21,34,54,81,117,166,229,309,411,537,691,880,1107,1377,1699,..
1,4,10,23,47,88,158,270,443,706,1094,1654,2450,3561,5087,7159,9936,13613,...
1,5,15,39,90,189,375,707,1276,2226,3768,6210,10002,15780,24432,...
1,6,21,61,156,361,781,1599,3124,5876,10696,18917,32627,55027,90948,...
1,7,28,90,252,635,1484,3267,6841,13744,26652,50108,91687,163772,286258,...
(End)
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
G. Almkvist, Asymptotic formulas and generalized Dedekind sums, Exper. Math., 7 (No. 4, 1998), pp. 343-359.
L. Carlitz, R. Scoville, A generating function for triangular partitions, Math. Comp. 29 (1975) 67-77
FORMULA
G.f.: 1/((1-x)^3*(1-x^3)^2*(1-x^5)).
MATHEMATICA
CoefficientList[Series[1/((1 - x)^3 (1 - x^3)^2 (1 - x^5)), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 29 2016 *)
PROG
(PARI) Vec(1/((1-x)^3*(1-x^3)^2*(1-x^5)) + O(x^50)) \\ Michel Marcus, Dec 08 2014
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)^3*(1-x^3)^2*(1-x^5)))); // Vincenzo Librandi, Aug 29 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jun 27 2003
STATUS
approved