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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 and A056000.

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

Cf. A000096, A056119, A056000, A001477.

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

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Last modified March 26 16:31 EDT 2017. Contains 284137 sequences.