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!)
A101859 a(n) = 11 + (23*n)/2 + n^2/2. 8
0, 11, 23, 36, 50, 65, 81, 98, 116, 135, 155, 176, 198, 221, 245, 270, 296, 323, 351, 380, 410, 441, 473, 506, 540, 575, 611, 648, 686, 725, 765, 806, 848, 891, 935, 980, 1026, 1073, 1121, 1170, 1220, 1271, 1323, 1376, 1430, 1485, 1541, 1598, 1656, 1715, 1775, 1836 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

COMMENTS

a(n+1) = A000096(n) + 9*n = A056126(n) + 2*n. - Zerinvary Lajos, Oct 01 2006

a(n) = A126890(n+1,10) for n>8. - Reinhard Zumkeller, Dec 30 2006

LINKS

Table of n, a(n) for n=-1..50.

C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube.

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

FORMULA

a(n) = C(n,2) - 10*n, n>=21. - Zerinvary Lajos, Nov 26 2006

G.f.: (11-10x)/(1-x)^3. - R. J. Mathar, Sep 09 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-1) = -f(n,n-1,11), for n>=1. - Milan Janjic, Dec 20 2008

a(n) = n + a(n-1) + 11 (with a(-1)=0). - Vincenzo Librandi, Nov 16 2010

a(n) = 11n - floor(n/2) + floor(n^2/2). - Wesley Ivan Hurt, Jun 15 2013

a(-1)=0, a(0)=11, a(1)=23, a(n)=3*a(n-1)-3*a(n-2)+a (n-3). - Harvey P. Dale, May 01 2016

EXAMPLE

G.f. = 11 + 23*x + 36*x^2 + 50*x^3 + 65*x^4 + 81*x^5 + 98*x^6 + 116*x^7 + ...

MAPLE

a:=n->sum(floor(k+2*n/(k+n)), k=10..n): seq(a(n), n=10..57); # Zerinvary Lajos, Oct 01 2006

[seq(binomial(n, 2)-10*n, n=21..72)]; # Zerinvary Lajos, Nov 26 2006

a:=n->sum(numer (k/(k+3)), k=11..n): seq(a(n), n=10..61); # Zerinvary Lajos, May 31 2008

with(finance):seq(add(cashflows([2, k, 8], 0 ), k=1..n), n=0..50); # Zerinvary Lajos, Jun 22 2008

MATHEMATICA

i=-10; 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 *)

Join[{0}, CoefficientList[Series[(11-10x)/(1-x)^3, {x, 0, 50}], x]] (* or *) LinearRecurrence[{3, -3, 1}, {0, 11, 23}, 60] (* Harvey P. Dale, May 01 2016 *)

PROG

(PARI) a(n)=11+(23*n)/2+n^2/2 \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. A000096, A056126, A001477.

Sequence in context: A017653 A180316 A139793 * A079664 A160268 A135978

Adjacent sequences:  A101856 A101857 A101858 * A101860 A101861 A101862

KEYWORD

easy,nonn

AUTHOR

Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 18 2004

EXTENSIONS

Edited by N. J. A. Sloane, Oct 07 2006

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 21 13:53 EST 2017. Contains 295001 sequences.