OFFSET
-1,2
LINKS
Cecilia 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) = A126890(n+1,10) for n>8. - Reinhard Zumkeller, Dec 30 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) = 11*n - 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
a(n+1) = n*(n + 21)/2. - Wolfdieter Lang, Oct 28 2020
From Amiram Eldar, Jan 10 2021: (Start)
Sum_{n>=0} (-1)^n/a(n) = 4*log(2)/21 - 166770367/2444321880. (End)
EXAMPLE
G.f. = 11 + 23*x + 36*x^2 + 50*x^3 + 65*x^4 + 81*x^5 + 98*x^6 + 116*x^7 + ...
MATHEMATICA
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
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