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%I #20 Apr 04 2024 09:49:41
%S 0,28,308,1218,3298,7250,13938,24388,39788,61488,91000,129998,180318,
%T 243958,323078,420000,537208,677348,843228,1037818,1264250,1525818,
%U 1825978,2168348,2556708,2995000,3487328,4037958,4651318,5331998,6084750
%N a(n) = 1*4*7 + 4*7*10 + 7*10*13 + ... (n terms).
%D Jolley, Summation of Series, Dover (1961), eq (49) page 10.
%H Vincenzo Librandi, <a href="/A196513/b196513.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1)
%F a(n) = ((3*n-2)*(3*n+1)*(3*n+4)*(3*n+7) + 56)/12 = n*(3*n+5)*(9*n^2 + 15*n - 10)/4 = Sum_{i=1..n} (3*i-2)*(3*i+1)*(3*i+4).
%F G.f.: -2*x*(14 + 84*x - 21*x^2 + 4*x^3) / (x-1)^5.
%o (Magma) [n*(3*n+5)*(9*n^2+15*n-10)/4 : n in [0..30]]; // _Vincenzo Librandi_, Oct 05 2011
%K nonn,easy
%O 0,2
%A _R. J. Mathar_, Oct 03 2011
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