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

%I A249911 #42 Aug 10 2025 20:10:13
%S A249911 0,1,60,177,352,585,876,1225,1632,2097,2620,3201,3840,4537,5292,6105,
%T A249911 6976,7905,8892,9937,11040,12201,13420,14697,16032,17425,18876,20385,
%U A249911 21952,23577,25260,27001,28800,30657,32572,34545,36576,38665,40812,43017,45280
%N A249911 60-gonal (hexacontagonal) numbers: a(n) = n(29n - 28).
%H A249911 Kelvin Voskuijl, <a href="/A249911/b249911.txt">Table of n, a(n) for n = 0..10000</a>
%H A249911 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Hexacontagon.html">Hexacontagon</a>.
%H A249911 <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>.
%H A249911 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A249911 G.f.: x^2*(1+57*x)/(1-x)^3. - _Vincenzo Librandi_, Nov 08 2014
%F A249911 a(n+1) = a(n) + 58*n  + 1. - _Jon Perry_, Nov 09 2014
%F A249911 E.g.f.: exp(x)*(x + 29*x^2). - _Nikolaos Pantelidis_, Feb 12 2023
%p A249911 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);
%t A249911 Table[n (29 n - 28), {n, 0, 60}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 1, 60}, 60]
%t A249911 CoefficientList[Series[x (1 + 57 x) / (1 - x)^3, {x, 0, 50}], x] (* _Vincenzo Librandi_, Nov 08 2014 *)
%t A249911 PolygonalNumber[60,Range[0,40]] (* _Harvey P. Dale_, Aug 16 2024 *)
%o A249911 (Magma) [n*(29*n-28): n in [0..50]]; // _Vincenzo Librandi_, Nov 08 2014
%o A249911 (PARI) a(n)=n*(29*n-28) \\ _Charles R Greathouse IV_, Nov 08 2014
%K A249911 nonn,easy
%O A249911 0,3
%A A249911 _K G Teal_, Nov 08 2014