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A056119 a(n) = n*(n+13)/2. 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

Table of n, a(n) for n=0..50.

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) = C(n,2) - 6*n, n>=13. - Zerinvary Lajos, Nov 25 2006

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

EXAMPLE

a(1) = 1+0+6 = 7; a(2) = 2+7+6 = 15; a(3) = 3+15+6 = 24. - Vincenzo Librandi, Aug 07 2010

MAPLE

a:=n->sum(floor(k+2*n/(k+n)), k=6..n): seq(a(n), n=5..55); # Zerinvary Lajos, Oct 01 2006

a:=n->sum(numer (k/(k+3)), k=7..n): seq(a(n), n=6..56); # Zerinvary Lajos, May 31 2008

with(finance):seq(add(cashflows([k, k, 12], 0 ), k=1..n)/2, n=0..45); # Zerinvary Lajos, Dec 22 2008

MATHEMATICA

i=-6; s=0; lst={}; Do[s+=n+i; If[s>=0, AppendTo[lst, s]], {n, 0, 6!, 1}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 29 2008 *)

PROG

(PARI) a(n)=n*(n+13)/2 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

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

Sequence in context: A113505 A184920 A076796 * A211430 A082111 A236582

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

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Last modified March 30 16:27 EDT 2017. Contains 284302 sequences.