A130876 Centered 1729-gonal numbers.

1, 1730, 5188, 10375, 17291, 25936, 36310, 48413, 62245, 77806, 95096, 114115, 134863, 157340, 181546, 207481, 235145, 264538, 295660, 328511, 363091, 399400, 437438, 477205, 518701, 561926, 606880, 653563, 701975, 752116, 803986, 857585, 912913

Offset: 0

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. A130859.

Programs

Maple

a:= n-> 1+(1729/2)*n*(1+n):
seq(a(n), n=0..35);  # Alois P. Heinz, Jul 16 2013

Mathematica

LinearRecurrence[{3,-3,1},{1,1730,5188},40] (* or *) Table[1+(1729/2)n(n+1), {n,0,40}] (* Harvey P. Dale, May 22 2017 *)

PARI

a(n) = 1 + (1729/2)*n + (1729/2)*n^2 \\ Michel Marcus, Jul 16 2013

Formula

a(n) = 1 + (1729/2)*n + (1729/2)*n^2.

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

G.f.: (1 + 1727*x + x^2)/(1-x)^3.

E.g.f.: exp(x)*(1 + 1729*x*(2 + x)/2).

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