A056119 a(n) = n*(n+13)/2.

0, 7, 15, 24, 34, 45, 57, 70, 84, 99, 115, 132, 150, 169, 189, 210, 232, 255, 279, 304, 330, 357, 385, 414, 444, 475, 507, 540, 574, 609, 645, 682, 720, 759, 799, 840, 882, 925, 969, 1014, 1060, 1107, 1155, 1204, 1254, 1305, 1357, 1410, 1464, 1519, 1575

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

P. Lafer, Discovering the square-triangular numbers, Fib. Quart., 9 (1971), 93-105.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

G.f.: x*(7-6*x)/(1-x)^3.

a(n) = A126890(n,6) for n > 5. - Reinhard Zumkeller, Dec 30 2006

a(n) = A000096(n) + 5*A001477(n) = A056115(n) + A001477(n) = A056121(n) - A001477(n). - Zerinvary Lajos, Feb 22 2008

If we define 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-1,7), for n >= 1. - Milan Janjic, Dec 20 2008

a(n) = n + a(n-1) + 6 (with a(0)=0). - Vincenzo Librandi, Aug 07 2010

Sum_{n>=1} 1/a(n) = 1145993/2342340 via A132759. - R. J. Mathar, Jul 14 2012

a(n) = 7*n - floor(n/2) + floor(n/2). - Wesley Ivan Hurt, Jun 15 2013

E.g.f.: x*(14 + x)*exp(x)/2. - G. C. Greubel, Jan 18 2020

Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/13 - 263111/2342340. - Amiram Eldar, Jan 10 2021

Prog

(PARI) a(n)=n*(n+13)/2 \\ Charles R Greathouse IV, Oct 07 2015
(Magma) [n*(n+13)/2: n in [0..50]]; // G. C. Greubel, Jan 18 2020
(Sage) [n*(n+13)/2 for n in (0..50)] # G. C. Greubel, Jan 18 2020
(GAP) List([0..50], n-> n*(n+13)/2 ); # G. C. Greubel, Jan 18 2020

Crossrefs

Cf. A000096, A001477, A056000, A056115, A056121.

Sequence in context: A113505 A184920 A076796 * A329383 A284758 A334798

Adjacent sequences: A056116 A056117 A056118 * A056120 A056121 A056122

Keyword

easy,nonn

Author

Barry E. Williams, Jul 04 2000

Extensions

More terms from James A. Sellers, Jul 05 2000

Status

approved