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%I #39 May 14 2023 14:45:39
%S 3,18,54,120,225,378,588,864,1215,1650,2178,2808,3549,4410,5400,6528,
%T 7803,9234,10830,12600,14553,16698,19044,21600,24375,27378,30618,
%U 34104,37845,41850,46128,50688,55539,60690,66150,71928,78033,84474,91260,98400,105903
%N Partial sums of n 3-spaced triangular numbers beginning with t(2), e.g., a(2) = t(2) + t(5) = 3 + 15 = 18.
%C Sums of rows of triangle A100345 (n>0).
%H Vincenzo Librandi, <a href="/A085789/b085789.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = 3/2 * n^2*(n+1).
%F a(n) = 3*n*binomial(n+1,2) = 3*n*A000217(n) = 3*A002411(n). - _Arkadiusz Wesolowski_, Feb 10 2012
%F G.f.: 3*(x + 2*x^2)/(1 - x)^4. - _Arkadiusz Wesolowski_, Feb 11 2012
%t CoefficientList[Series[3 (1 + 2 x) / (1 - x)^4, {x, 0, 40}], x](* _Vincenzo Librandi_, Aug 14 2017 *)
%t LinearRecurrence[{4,-6,4,-1},{3,18,54,120},50] (* _Harvey P. Dale_, May 14 2023 *)
%o (Magma) [3/2*n^2*(n+1): n in [1..40]]; // _Vincenzo Librandi_, Aug 14 2017
%Y Cf. A004188.
%K nonn,easy
%O 1,1
%A _Jon Perry_, Jul 23 2003
%E More terms from _Reinhard Zumkeller_, Nov 18 2004
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