login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A056115 a(n) = n*(n+11)/2. 15
0, 6, 13, 21, 30, 40, 51, 63, 76, 90, 105, 121, 138, 156, 175, 195, 216, 238, 261, 285, 310, 336, 363, 391, 420, 450, 481, 513, 546, 580, 615, 651, 688, 726, 765, 805, 846, 888, 931, 975, 1020, 1066, 1113, 1161, 1210, 1260, 1311, 1363, 1416, 1470, 1525 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

LINKS

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

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

FORMULA

G.f.: x(6-5x)/(1-x)^3.

a(n) = A000096(n) + 4*A001477(n) = A056000(n) + A001477(n) = A056119(n) - A001477(n). - Zerinvary Lajos, Oct 01 2006

a(n) = C(n,2)-5*n, for n>=11. - Zerinvary Lajos, Nov 25 2006

a(n) = A126890(n,5) for n>4. - Reinhard Zumkeller, Dec 30 2006

Equals A119412/2. - Zerinvary Lajos, Feb 12 2007

If we define f(n,i,a)=sum(binomial(n,k)*stirling1(n-k,i)*product(-a-j,j=0..k-1),k=0..n-i), then a(n) = -f(n,n-1,6), for n>=1. - Milan Janjic, Dec 20 2008

a(n) = n+a(n-1)+5 (with a(0)=0). - Vincenzo Librandi, Aug 07 2010

sum_{n>=1} 1/a(n) = 83711/152460. - R. J. Mathar, Jul 14 2012

a(n) = 6n - floor(n/2) + floor(n^2/2). - Wesley Ivan Hurt, Jun 15 2013

MAPLE

a:=n->sum(floor(k+2*n/(k+n)), k=5..n): seq(a(n), n=4..53); # Zerinvary Lajos, Oct 01 2006

[seq(binomial(n, 2)-5*n, n=11..61)]; # Zerinvary Lajos, Nov 25 2006

a:=n->sum(numer (k/(k+3)), k=6..n): seq(a(n), n=5..55); # Zerinvary Lajos, May 31 2008

with(finance):seq(add(cashflows([k, k, 10], 0 ), k=1..n)/2, n=0..45); # Zerinvary Lajos, Dec 22 2008

MATHEMATICA

s=0; lst={s}; Do[s+=n+1; AppendTo[lst, s], {n, 5, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 25 2008 *)

PROG

(PARI) a(n)=n*(n+11)/2; \\ Joerg Arndt, Oct 25 2014

CROSSREFS

Cf. A055999, A056000, A000096, A056119, A001477.

Third column of Pascal (1, 6) triangle A096956.

Sequence in context: A017053 A046040 A227359 * A173358 A101247 A243655

Adjacent sequences:  A056112 A056113 A056114 * A056116 A056117 A056118

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Jul 04 2000

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 22 05:36 EST 2017. Contains 295076 sequences.