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%I #24 Feb 10 2023 04:37:10
%S 0,1,38,111,220,365,546,763,1016,1305,1630,1991,2388,2821,3290,3795,
%T 4336,4913,5526,6175,6860,7581,8338,9131,9960,10825,11726,12663,13636,
%U 14645,15690,16771,17888,19041,20230,21455,22716,24013,25346,26715,28120,29561
%N 38-gonal numbers: a(n) = n*(18*n-17).
%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 G.f.: -x*(35*x+1)/(x-1)^3.
%F E.g.f.: exp(x)*(x + 18*x^2). - _Nikolaos Pantelidis_, Feb 10 2023
%t Table[n(36n-34)/2, {n,50}]
%t LinearRecurrence[{3, -3, 1}, {0, 1, 38}, 42] (* or *) CoefficientList[Series[-x * (35 * x + 1) / (x - 1) ^ 3, {x, 0, 41}], x] (* _Indranil Ghosh_, Feb 27 2017 *)
%o (PARI) for(n=0,20,print1(n*(18*n-17),", ")) \\ _Derek Orr_, Feb 26 2017
%o (PARI) a(n)=n*(18*n-17) \\ _Charles R Greathouse IV_, Feb 26 2017
%Y Cf. A255187, A254474, A261191.
%K nonn,easy
%O 0,3
%A _Haney Moon_, Feb 23 2017
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