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%I #25 Sep 08 2022 08:46:05
%S 0,2,19,51,98,160,237,329,436,558,695,847,1014,1196,1393,1605,1832,
%T 2074,2331,2603,2890,3192,3509,3841,4188,4550,4927,5319,5726,6148,
%U 6585,7037,7504,7986,8483,8995,9522,10064,10621,11193,11780,12382,12999,13631,14278
%N a(n) = n*(15*n-11)/2.
%C Sum of n-th 9-gonal (nonagonal) number and n-th 10-gonal (decagonal) number.
%C Sum of reciprocals of a(n), for n>0: 0.614629940137818703272919217222307...
%H Bruno Berselli, <a href="/A226489/b226489.txt">Table of n, a(n) for n = 0..1000</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*(2+13*x)/(1-x)^3.
%F a(n) + a(-n) = A064761(n).
%t Table[n (15 n - 11)/2, {n, 0, 50}]
%t CoefficientList[Series[x (2 + 13 x) / (1 - x)^3, {x, 0, 45}], x] (* _Vincenzo Librandi_, Aug 18 2013 *)
%o (Magma) [n*(15*n-11)/2: n in [0..50]];
%o (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 (PARI) a(n)=n*(15*n-11)/2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A001106, A001107.
%Y Cf. numbers of the form n*(n*k-k+4))/2, this sequence is the case k=15: see list in A226488.
%K nonn,easy
%O 0,2
%A _Bruno Berselli_, Jun 09 2013
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