A249911 60-gonal (hexacontagonal) numbers: a(n) = n(29n - 28).

0, 1, 60, 177, 352, 585, 876, 1225, 1632, 2097, 2620, 3201, 3840, 4537, 5292, 6105, 6976, 7905, 8892, 9937, 11040, 12201, 13420, 14697, 16032, 17425, 18876, 20385, 21952, 23577, 25260, 27001, 28800, 30657, 32572, 34545, 36576, 38665, 40812, 43017, 45280

Offset

0,3

Links

Table of n, a(n) for n=0..40.

Eric Weisstein's World of Mathematics, Hexacontagon.

Index to sequences related to polygonal numbers.

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

Formula

G.f.: x^2*(1+57*x)/(1-x)^3. - Vincenzo Librandi, Nov 08 2014

a(n+1) = a(n) + 58*n + 1. - Jon Perry, Nov 09 2014

E.g.f.: exp(x)*(x + 29*x^2). - Nikolaos Pantelidis, Feb 12 2023

Maple

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]-a[n-2]+58 od: seq(a[n], n=0..46);

Mathematica

Table[n (29 n - 28), {n, 0, 60}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 1, 60}, 60]
CoefficientList[Series[x (1 + 57 x) / (1 - x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Nov 08 2014 *)
PolygonalNumber[60, Range[0, 40]] (* Harvey P. Dale, Aug 16 2024 *)

Prog

(Magma) [n*(29*n-28): n in [0..50]]; // Vincenzo Librandi, Nov 08 2014
(PARI) a(n)=n*(29*n-28) \\ Charles R Greathouse IV, Nov 08 2014

Crossrefs

Sequence in context: A257146 A291549 A259946 * A292223 A112827 A181333

Adjacent sequences: A249908 A249909 A249910 * A249912 A249913 A249914

Keyword

nonn,easy

Author

K G Teal, Nov 08 2014

Status

approved