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

Author

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

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A130876.

Programs

Mathematica

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

PARI

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

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)