A282850 - OEIS

%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