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
Links
- Kelvin Voskuijl, Table of n, a(n) for n = 0..10000
- 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).
Programs
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Magma
[n*(29*n-28): n in [0..50]]; // Vincenzo Librandi, Nov 08 2014
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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);
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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 *) -
PARI
a(n)=n*(29*n-28) \\ Charles R Greathouse IV, Nov 08 2014
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