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%I #21 Feb 10 2023 04:54:12
%S 0,1,34,99,196,325,486,679,904,1161,1450,1771,2124,2509,2926,3375,
%T 3856,4369,4914,5491,6100,6741,7414,8119,8856,9625,10426,11259,12124,
%U 13021,13950,14911,15904,16929,17986,19075,20196,21349,22534,23751
%N 34-gonal numbers: a(n) = n*(32*n-30)/2.
%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 From _Nikolaos Pantelidis_, Feb 09 2023 : (Start)
%F G.f.: x*(1 + 31*x)/(1 - x)^3.
%F E.g.f.: exp(x)*(x + 16*x^2). (End)
%t Table[n(32n-30)/2, {n,50}]
%t PolygonalNumber[34,Range[0,40]] (* or *) LinearRecurrence[{3,-3,1},{0,1,34},40] (* The first program requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 26 2018 *)
%o (PARI) a(n)=n*(16*n-15) \\ _Charles R Greathouse IV_, Feb 27 2017
%Y Cf. A246645, A254474, A261191.
%K nonn,easy
%O 0,3
%A _Daniel Mohebiravesh_, Feb 23 2017