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%I #40 Feb 10 2023 06:05:15
%S 0,1,33,96,190,315,471,658,876,1125,1405,1716,2058,2431,2835,3270,
%T 3736,4233,4761,5320,5910,6531,7183,7866,8580,9325,10101,10908,11746,
%U 12615,13515,14446,15408,16401,17425,18480,19566,20683,21831,23010
%N 33-gonal numbers: n(31n-29)/2.
%C Similar to 21-gonal and 15-gonal numbers (A051873, A051867).
%H Daniel Starodubtsev, <a href="/A098923/b098923.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = n*(31*n-29)/2.
%F G.f.: x*(1+30*x)/(1-x)^3. - _Bruno Berselli_, Feb 04 2011
%F a(n) = 31*n + a(n-1) - 30 (with a(0)=0). - _Vincenzo Librandi_, Nov 16 2010
%F E.g.f.: exp(x)*(x + 31*x^2/2). - _Nikolaos Pantelidis_, Feb 10 2023
%t Table[n(31n - 29)/2, {n, 0, 40}] (* _Stefan Steinerberger_, Feb 15 2006 *)
%t PolygonalNumber[33,Range[0,40]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Mar 02 2018 *)
%o (PARI) a(n)=n*(31*n-29)/2 \\ _Charles R Greathouse IV_, Oct 16 2015
%Y Cf. A051867, A051873.
%K nonn,easy
%O 0,3
%A _Parthasarathy Nambi_, Oct 18 2004
%E More terms from _Stefan Steinerberger_, Feb 15 2006
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