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A226489 a(n) = n*(15*n-11)/2.

%I A226489 #31 Jan 12 2025 21:18:56
%S A226489 0,2,19,51,98,160,237,329,436,558,695,847,1014,1196,1393,1605,1832,
%T A226489 2074,2331,2603,2890,3192,3509,3841,4188,4550,4927,5319,5726,6148,
%U A226489 6585,7037,7504,7986,8483,8995,9522,10064,10621,11193,11780,12382,12999,13631,14278,14940
%N A226489 a(n) = n*(15*n-11)/2.
%C A226489 Sum of n-th 9-gonal (nonagonal) number and n-th 10-gonal (decagonal) number.
%C A226489 Sum of reciprocals of a(n), for n > 0: 0.614629940137818703272919217222307...
%H A226489 Bruno Berselli, <a href="/A226489/b226489.txt">Table of n, a(n) for n = 0..1000</a>
%H A226489 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A226489 G.f.: x*(2+13*x)/(1-x)^3.
%F A226489 a(n) + a(-n) = A064761(n).
%F A226489 From _Elmo R. Oliveira_, Jan 12 2025: (Start)
%F A226489 E.g.f.: exp(x)*x*(4 + 15*x)/2.
%F A226489 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A226489 Table[n (15 n - 11)/2, {n, 0, 50}]
%t A226489 CoefficientList[Series[x (2 + 13 x) / (1 - x)^3, {x, 0, 45}], x] (* _Vincenzo Librandi_, Aug 18 2013 *)
%o A226489 (Magma) [n*(15*n-11)/2: n in [0..50]];
%o A226489 (Magma) I:=[0,2,19]; [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 A226489 (PARI) a(n)=n*(15*n-11)/2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A226489 Cf. A001106, A001107, A064761.
%Y A226489 Cf. numbers of the form n*(n*k - k + 4)/2, this sequence is the case k=15: see list in A226488.
%K A226489 nonn,easy
%O A226489 0,2
%A A226489 _Bruno Berselli_, Jun 09 2013