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 A101859 a(n) = 11 + (23*n)/2 + n^2/2. 8

%I

%S 0,11,23,36,50,65,81,98,116,135,155,176,198,221,245,270,296,323,351,

%T 380,410,441,473,506,540,575,611,648,686,725,765,806,848,891,935,980,

%U 1026,1073,1121,1170,1220,1271,1323,1376,1430,1485,1541,1598,1656,1715,1775,1836

%N a(n) = 11 + (23*n)/2 + n^2/2.

%C a(n+1) = A000096(n) + 9*n = A056126(n) + 2*n. - _Zerinvary Lajos_, Oct 01 2006

%C a(n) = A126890(n+1,10) for n>8. - _Reinhard Zumkeller_, Dec 30 2006

%H C. Rossiter, <a href="http://noticingnumbers.net/300SeriesCube.htm">Depictions, Explorations and Formulas of the Euler/Pascal Cube</a>.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = C(n,2) - 10*n, n>=21. - _Zerinvary Lajos_, Nov 26 2006

%F G.f.: (11-10x)/(1-x)^3. - _R. J. Mathar_, Sep 09 2008

%F 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

%F a(n) = n + a(n-1) + 11 (with a(-1)=0). - _Vincenzo Librandi_, Nov 16 2010

%F a(n) = 11n - floor(n/2) + floor(n^2/2). - _Wesley Ivan Hurt_, Jun 15 2013

%F 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

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

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

%p [seq(binomial(n,2)-10*n,n=21..72)]; # _Zerinvary Lajos_, Nov 26 2006

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

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

%t 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 *)

%t 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 *)

%o (PARI) a(n)=11+(23*n)/2+n^2/2 \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. A000096, A056126, A001477.

%K easy,nonn

%O -1,2

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

%E Edited by _N. J. A. Sloane_, Oct 07 2006

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