A130859 1729-gonal numbers.

1, 1729, 5184, 10366, 17275, 25911, 36274, 48364, 62181, 77725, 94996, 113994, 134719, 157171, 181350, 207256, 234889, 264249, 295336, 328150, 362691, 398959, 436954, 476676, 518125, 561301, 606204, 652834, 701191, 751275, 803086, 856624, 911889, 968881, 1027600, 1088046, 1150219

Offset

1,2

Links

Table of n, a(n) for n=1..37.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = (1727*n^2 - 1725*n)/2.

From Elmo R. Oliveira, Nov 27 2024: (Start)

G.f.: x*(1 + 1726*x)/(1-x)^3.

E.g.f.: exp(x)*x*(2 + 1727*x)/2.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)

Mathematica

PolygonalNumber[1729, Range[40]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 15 2016 *)

Prog

(PARI) a(n) = (1727*n^2 - 1725*n)/2 \\ Michel Marcus, Jul 16 2013

Crossrefs

Cf. A130876.

Sequence in context: A018850 A062924 A350270 * A245671 A154716 A375322

Adjacent sequences: A130856 A130857 A130858 * A130860 A130861 A130862

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 06 2007, based on a suggestion from Anton Mravcek in 2004.

Status

approved