OFFSET
0,2
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: x*(6-5*x)/(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) = 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_{k=0..n-i} ( binomial(n,k)*stirling1(n-k,i) *Product_{j=0..k-1} (-a-j) ), then a(n) = -f(n,n-1,6), for n>=1. - Milan Janjic, Dec 20 2008
a(n) = a(n-1) + n + 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) = 6*n - floor(n/2) + floor(n^2/2). - Wesley Ivan Hurt, Jun 15 2013
E.g.f.: x*(12 + x)*exp(x)/2. - G. C. Greubel, Jan 18 2020
Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/11 - 20417/152460. - Amiram Eldar, Jan 10 2021
MATHEMATICA
((2*Range[0, 50]+11)^2 -11^2)/8 (* G. C. Greubel, Jan 18 2020 *)
PROG
(PARI) a(n)=n*(n+11)/2; \\ Joerg Arndt, Oct 25 2014
(Magma) [n*(n+11)/2: n in [0..50]]; // G. C. Greubel, Jan 18 2020
(Sage) [n*(n+11)/2 for n in (0..50)] # G. C. Greubel, Jan 18 2020
(GAP) List([0..50], n-> n*(n+11)/2 ); # G. C. Greubel, Jan 18 2020
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Jul 04 2000
STATUS
approved