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%I #24 Feb 01 2023 19:24:47
%S 0,2,25,69,134,220,327,455,604,774,965,1177,1410,1664,1939,2235,2552,
%T 2890,3249,3629,4030,4452,4895,5359,5844,6350,6877,7425,7994,8584,
%U 9195,9827,10480,11154,11849,12565,13302,14060,14839,15639,16460,17302,18165,19049
%N a(n) = n*(21*n-17)/2.
%C Sum of n-th dodecagonal number and n-th tridecagonal number.
%C Sum of reciprocals of a(n), for n>0: 0.58517199913243139233033474262449...
%H Bruno Berselli, <a href="/A226491/b226491.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+19*x)/(1-x)^3.
%F a(n) + a(-n) = A064762(n).
%t Table[n (21 n - 17)/2, {n, 0, 50}]
%t CoefficientList[Series[x (2 + 19 x) / (1 - x)^3, {x, 0, 45}], x] (* _Vincenzo Librandi_, Aug 18 2013 *)
%t LinearRecurrence[{3,-3,1},{0,2,25},50] (* _Harvey P. Dale_, Feb 01 2023 *)
%o (Magma) [n*(21*n-17)/2: n in [0..50]];
%o (Magma) I:=[0,2,25]; [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*(21*n-17)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A051624, A051865.
%Y Cf. numbers of the form n*(n*k-k+4))/2, this sequence is the case k=21: see list in A226488.
%K nonn,easy
%O 0,2
%A _Bruno Berselli_, Jun 09 2013
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