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

0,2

Links

Table of n, a(n) for n=0..32.

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

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)

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 *)

Prog

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

Crossrefs

Cf. A130859.

Sequence in context: A339909 A339878 A258166 * A234706 A211853 A252454

Adjacent sequences: A130873 A130874 A130875 * A130877 A130878 A130879

Keyword

nonn,easy

Author

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

Status

approved