A098140 63-gonal numbers: a(n) = n*(61*n - 59)/2.

0, 1, 63, 186, 370, 615, 921, 1288, 1716, 2205, 2755, 3366, 4038, 4771, 5565, 6420, 7336, 8313, 9351, 10450, 11610, 12831, 14113, 15456, 16860, 18325, 19851, 21438, 23086, 24795, 26565, 28396, 30288, 32241, 34255, 36330, 38466

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index to sequences related to polygonal numbers

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

Formula

a(n) = n*(61*n - 59)/2.

G.f.: x*(1 + 60*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011

a(0)=0, a(1)=1, a(2)=63, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Jun 09 2011

E.g.f.: exp(x)*(x + 61*x^2/2). - Nikolaos Pantelidis, Feb 10 2023

Mathematica

Table[n(61n - 59)/2, {n, 0, 50}] (* Stefan Steinerberger, Feb 28 2006 *)
LinearRecurrence[{3, -3, 1}, {0, 1, 63}, 50] (* Harvey P. Dale, Jun 09 2011 *)
CoefficientList[Series[x (1 + 60 x) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 16 2017 *)

Prog

(PARI) a(n)=n*(61*n-59)/2 \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [(61*n^2-59*n)/2: n in [0..40]]; // Vincenzo Librandi, Aug 16 2017

Crossrefs

Sequence in context: A044395 A044776 A077263 * A008895 A359563 A008874

Adjacent sequences: A098137 A098138 A098139 * A098141 A098142 A098143

Keyword

nonn,easy

Author

Parthasarathy Nambi, Oct 25 2004

Extensions

More terms from Stefan Steinerberger, Feb 28 2006

Offset corrected by Eric Rowland, Aug 15 2017

Status

approved