OFFSET
0,2
COMMENTS
Partial sums of A147875.
Equals the fourth right hand column of A175136 for n>=1. - Johannes W. Meijer, May 06 2011
a(n) is the number of triples (w,x,y) havingt all terms in {0,...,n} and x+y>w. - Clark Kimberling, Jun 14 2012
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
From Johannes W. Meijer, May 06 2011: (Start)
G.f.: x*(4+x)/(1-x)^4.
a(n) = 4*binomial(n+2,3) + binomial(n+1,3).
a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4), a(0)=0, a(1)=4, a(2)=17, a(3)=44. - Harvey P. Dale, May 20 2014
E.g.f.: x*(24 +27*x +5*x^2)*exp(x)/6. - G. C. Greubel, Mar 31 2021
MAPLE
MATHEMATICA
Table[(n(n+1)(5n+7))/6, {n, 0, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 4, 17, 44}, 50] (* Harvey P. Dale, May 20 2014 *)
PROG
(Magma) [n*(n+1)*(5*n+7)/6: n in [0..50]]; // Vincenzo Librandi, May 07 2011
(PARI) a(n)=n*(n+1)*(5*n+7)/6 \\ Charles R Greathouse IV, Oct 07 2015
(Sage) [n*(n+1)*(5*n+7)/6 for n in (0..50)] # G. C. Greubel, Mar 31 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, Jun 25 2009
EXTENSIONS
Definition rephrased by R. J. Mathar, Jun 27 2009
STATUS
approved