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%I #31 Jan 15 2021 06:04:46
%S 0,17,36,57,80,105,132,161,192,225,260,297,336,377,420,465,512,561,
%T 612,665,720,777,836,897,960,1025,1092,1161,1232,1305,1380,1457,1536,
%U 1617,1700,1785,1872,1961,2052,2145,2240,2337,2436,2537,2640,2745,2852,2961
%N a(n) = n*(n + 16).
%H G. C. Greubel, <a href="/A098849/b098849.txt">Table of n, a(n) for n = 0..1000</a>
%H Felix P. Muga II, <a href="https://www.researchgate.net/publication/267327689">Extending the Golden Ratio and the Binet-de Moivre Formula</a>, Preprint on ResearchGate, March 2014.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = (n+8)^2 - 8^2 = n*(n + 16), n>=0.
%F G.f.: x*(17 - 15*x)/(1-x)^3.
%F a(n) = a(n-1) + 2*n + 15 (with a(0)=0). - _Vincenzo Librandi_, Nov 17 2010
%F From _G. C. Greubel_, Jul 29 2016: (Start)
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F E.g.f.: x*(17 + x)*exp(x). (End)
%F From _Amiram Eldar_, Jan 15 2021: (Start)
%F Sum_{n>=1} 1/a(n) = H(16)/16 = A001008(16)/A102928(16) = 2436559/11531520, where H(k) is the k-th harmonic number.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 95549/2306304. (End)
%p seq(n*(n+16),n=0..55); # _Emeric Deutsch_, Mar 26 2005
%p a:=n->sum(n, j=17..n): seq(a(n), n=16..63); # _Zerinvary Lajos_, Feb 17 2008
%t s=0;lst={};Do[s+=n;AppendTo[lst,s],{n,17,6!,2}];lst (* _Vladimir Joseph Stephan Orlovsky_, Feb 26 2009 *)
%t LinearRecurrence[{3, -3, 1}, {0, 17, 36}, 50] (* _G. C. Greubel_, Jul 29 2016 *)
%o (PARI) a(n)=n*(n+16) \\ _Charles R Greathouse IV_, Jul 30 2016
%Y Cf. A001008, A098832, A001477, A056126, A102928, A120071, A132760, A132761, A132765.
%Y a(n-8), n>=9, eighth column (used for the n=8 series of the hydrogen atom) of triangle A120070.
%K nonn,easy
%O 0,2
%A Eugene McDonnell (eemcd(AT)mac.com), Nov 04 2004
%E More terms from _Emeric Deutsch_, Mar 26 2005
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