A098849 a(n) = n*(n + 16).

0, 17, 36, 57, 80, 105, 132, 161, 192, 225, 260, 297, 336, 377, 420, 465, 512, 561, 612, 665, 720, 777, 836, 897, 960, 1025, 1092, 1161, 1232, 1305, 1380, 1457, 1536, 1617, 1700, 1785, 1872, 1961, 2052, 2145, 2240, 2337, 2436, 2537, 2640, 2745, 2852, 2961

Offset: 0

Author

Eugene McDonnell (eemcd(AT)mac.com), Nov 04 2004

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Felix P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, Preprint on ResearchGate, March 2014.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A001008, A098832, A001477, A056126, A102928, A120071, A132760, A132761, A132765.

a(n-8), n>=9, eighth column (used for the n=8 series of the hydrogen atom) of triangle A120070.

Programs

Maple

seq(n*(n+16),n=0..55); # Emeric Deutsch, Mar 26 2005
a:=n->sum(n, j=17..n): seq(a(n), n=16..63); # Zerinvary Lajos, Feb 17 2008

Mathematica

s=0;lst={};Do[s+=n;AppendTo[lst,s],{n,17,6!,2}];lst (* Vladimir Joseph Stephan Orlovsky, Feb 26 2009 *)
LinearRecurrence[{3, -3, 1}, {0, 17, 36}, 50] (* G. C. Greubel, Jul 29 2016 *)
Table[n(n+16),{n,0,50}] (* Harvey P. Dale, Jul 18 2024 *)

PARI

a(n)=n*(n+16) \\ Charles R Greathouse IV, Jul 30 2016

Formula

a(n) = (n+8)^2 - 8^2 = n*(n + 16), n>=0.

G.f.: x*(17 - 15*x)/(1-x)^3.

a(n) = a(n-1) + 2*n + 15 (with a(0)=0). - Vincenzo Librandi, Nov 17 2010

From G. C. Greubel, Jul 29 2016: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

E.g.f.: x*(17 + x)*exp(x). (End)

From Amiram Eldar, Jan 15 2021: (Start)

Sum_{n>=1} 1/a(n) = H(16)/16 = A001008(16)/A102928(16) = 2436559/11531520, where H(k) is the k-th harmonic number.

Sum_{n>=1} (-1)^(n+1)/a(n) = 95549/2306304. (End)

Extensions

More terms from Emeric Deutsch, Mar 26 2005