A120071 a(n) = n*(n+20).

0, 21, 44, 69, 96, 125, 156, 189, 224, 261, 300, 341, 384, 429, 476, 525, 576, 629, 684, 741, 800, 861, 924, 989, 1056, 1125, 1196, 1269, 1344, 1421, 1500, 1581, 1664, 1749, 1836, 1925, 2016, 2109, 2204, 2301, 2400, 2501, 2604, 2709, 2816, 2925, 3036, 3149, 3264

Offset

0,2

Links

Table of n, a(n) for n=0..48.

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).

Formula

a(n) = (n+10)^2 - 10^2 = n*(n+20), n>=0.

G.f.: x*(21-19*x)/(1-x)^3.

a(n) = 2*n + a(n-1) + 19 (with a(0)=0). - Vincenzo Librandi, Nov 13 2010

From Amiram Eldar, Jan 16 2021: (Start)

Sum_{n>=1} 1/a(n) = H(20)/20 = A001008(20)/A102928(20) = 11167027/62078016, where H(k) is the k-th harmonic number.

Sum_{n>=1} (-1)^(n+1)/a(n) = 155685007/4655851200. (End)

Maple

seq(sum(4*k-n, k=7..n), n=6..51); # Zerinvary Lajos, Feb 17 2008

Mathematica

s=0; lst={}; Do[s+=n; AppendTo[lst, s], {n, 21, 6!, 2}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 26 2009 *)

Prog

(PARI) a(n)=n*(n+20) \\ Charles R Greathouse IV, Jan 21 2015

Crossrefs

a(n-10), n>=11, tenth column (used for the n=10 series of the hydrogen atom) of triangle A120070.

For n*(n+18) see A098850.

Cf. A001008, A001477, A098849, A102928, A120061, A132765, A132760, A132761, A132762, A005563, A028552, A028347, A028557, A028560, A028563, A028566, A028569, A098603, A098847, A132759, A098848.

Sequence in context: A041880 A359880 A063319 * A168519 A003857 A317210

Adjacent sequences: A120068 A120069 A120070 * A120072 A120073 A120074

Keyword

nonn,easy

Author

Wolfdieter Lang, Jul 20 2006

Status

approved