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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 *)

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

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Last modified March 24 15:46 EDT 2017. Contains 283991 sequences.