A098923 33-gonal numbers: n(31n-29)/2.

0, 1, 33, 96, 190, 315, 471, 658, 876, 1125, 1405, 1716, 2058, 2431, 2835, 3270, 3736, 4233, 4761, 5320, 5910, 6531, 7183, 7866, 8580, 9325, 10101, 10908, 11746, 12615, 13515, 14446, 15408, 16401, 17425, 18480, 19566, 20683, 21831, 23010

Offset: 0

Author

Parthasarathy Nambi, Oct 18 2004

Keywords

• nonn
• easy

Comments

Similar to 21-gonal and 15-gonal numbers (A051873, A051867).

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 0..10000
• Index to sequences related to polygonal numbers
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A051867, A051873.

Programs

Mathematica

Table[n(31n - 29)/2, {n, 0, 40}] (* Stefan Steinerberger, Feb 15 2006 *)
PolygonalNumber[33,Range[0,40]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 02 2018 *)

PARI

a(n)=n*(31*n-29)/2 \\ Charles R Greathouse IV, Oct 16 2015

Formula

a(n) = n*(31*n-29)/2.

G.f.: x*(1+30*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011

a(n) = 31*n + a(n-1) - 30 (with a(0)=0). - Vincenzo Librandi, Nov 16 2010

E.g.f.: exp(x)*(x + 31*x^2/2). - Nikolaos Pantelidis, Feb 10 2023

Extensions

More terms from Stefan Steinerberger, Feb 15 2006