A084439 Number of triangular partitions of n of order 3.

1, 3, 6, 12, 21, 34, 54, 81, 117, 166, 229, 309, 411, 537, 691, 880, 1107, 1377, 1699, 2077, 2518, 3033, 3627, 4309, 5092, 5983, 6993, 8137, 9424, 10867, 12484, 14286, 16288, 18511, 20968, 23677, 26662, 29938, 33526, 37453, 41737, 46402, 51478, 56986, 62953, 69413

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

Cf. A001840, A084446, A084447.

Sequence in context: A070333 A011779 A161809 * A034344 A260640 A203292

Adjacent sequences: A084436 A084437 A084438 * A084440 A084441 A084442

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 27 2003

Status

approved