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A226490 a(n) = n*(19*n-15)/2.

%I A226490 #27 Dec 28 2024 10:18:42
%S A226490 0,2,23,63,122,200,297,413,548,702,875,1067,1278,1508,1757,2025,2312,
%T A226490 2618,2943,3287,3650,4032,4433,4853,5292,5750,6227,6723,7238,7772,
%U A226490 8325,8897,9488,10098,10727,11375,12042,12728,13433,14157,14900,15662,16443,17243,18062
%N A226490 a(n) = n*(19*n-15)/2.
%C A226490 Sum of n-th hendecagonal number and n-th dodecagonal number.
%C A226490 Sum of reciprocals of a(n), for n > 0: 0.59314195720519963010713286193275...
%H A226490 Bruno Berselli, <a href="/A226490/b226490.txt">Table of n, a(n) for n = 0..1000</a>
%H A226490 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A226490 G.f.: x*(2+17*x)/(1-x)^3.
%F A226490 From _Elmo R. Oliveira_, Dec 27 2024: (Start)
%F A226490 E.g.f.: exp(x)*x*(4 + 19*x)/2.
%F A226490 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
%F A226490 a(n) = n + A051873(n). (End)
%t A226490 Table[n (19 n - 15)/2, {n, 0, 50}]
%t A226490 CoefficientList[Series[x (2 + 17 x) / (1 - x)^3, {x, 0, 45}], x] (* _Vincenzo Librandi_, Aug 18 2013 *)
%t A226490 LinearRecurrence[{3,-3,1},{0,2,23},50] (* _Harvey P. Dale_, Aug 17 2017 *)
%o A226490 (Magma) [n*(19*n-15)/2: n in [0..50]];
%o A226490 (Magma) I:=[0,2,23]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..45]]; // _Vincenzo Librandi_, Aug 18 2013
%o A226490 (PARI) a(n)=n*(19*n-15)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A226490 Cf. A051624, A051682, A051873.
%Y A226490 Cf. numbers of the form n*(n*k - k + 4)/2, this sequence is the case k=19: see list in A226488.
%K A226490 nonn,easy
%O A226490 0,2
%A A226490 _Bruno Berselli_, Jun 09 2013