A056121 a(n) = n*(n + 15)/2.

0, 8, 17, 27, 38, 50, 63, 77, 92, 108, 125, 143, 162, 182, 203, 225, 248, 272, 297, 323, 350, 378, 407, 437, 468, 500, 533, 567, 602, 638, 675, 713, 752, 792, 833, 875, 918, 962, 1007, 1053, 1100, 1148, 1197, 1247, 1298, 1350, 1403, 1457, 1512, 1568, 1625

Offset: 0

Author

Barry E. Williams, Jul 06 2000

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000096, A001477, A056000, A056119, A056126.

Programs

GAP

List([0..60], n-> n*(n+15)/2 ); # G. C. Greubel, Jan 18 2020

Magma

[n*(n+15)/2: n in [0..60]]; // G. C. Greubel, Jan 18 2020

Maple

a:=n->n*(n+15)/2: seq(a(n),n=0..60);

Mathematica

Table[n*(n + 15)/2, {n, 0, 100}] (* Paolo Xausa, Aug 02 2024 *)

PARI

a(n)=n*(n+15)/2 \\ Charles R Greathouse IV, Sep 24 2015

Sage

[n*(n+15)/2 for n in (0..60)] # G. C. Greubel, Jan 18 2020

Formula

G.f.: x*(8-7*x)/(1-x)^3.

a(n) = A000096(n) + 6*n = A056119(n) + n = A056126(n) - n. - Zerinvary Lajos, Oct 01 2006

a(n-15) = binomial(n,2) - 7*n. - Zerinvary Lajos, Nov 26 2006

a(n) = A126890(n,7) for n>6. - Reinhard Zumkeller, Dec 30 2006

Let f(n,i,a) = Sum_{k=0..n-i} binomial(n,k)*Stirling1(n-k,i)*Product_{j=0..k-1} (-a-j), then a(n) = -f(n,n-1,8), for n>=1. - Milan Janjic, Dec 20 2008

a(n) = a(n-1)+ n + 7 (with a(0)=0). - Vincenzo Librandi, Aug 07 2010

Sum_{n>=1} 1/a(n) = 1195757/2702700 via A132760. - R. J. Mathar, Jul 14 2012

a(n) = 8*n - floor(n/2) + floor(n^2/2). - Wesley Ivan Hurt, Jun 15 2013

E.g.f.: x*(16 + x)*exp(x)/2. - G. C. Greubel, Jan 18 2020

Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/15 - 52279/540540. - Amiram Eldar, Jan 10 2021

Extensions

More terms from James Sellers, Jul 07 2000