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A098140
63-gonal numbers: a(n) = n*(61*n - 59)/2.
1
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
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
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