OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1350 (terms 0..136 from Vincenzo Librandi)
Index entries for linear recurrences with constant coefficients, signature (5,2,1).
FORMULA
a(n) = Sum_{k=0..n} binomial(3*n-k+1,3*n-3*k+1).
G.f.: (1-x-x^2)/(1-5*x-2*x^2-x^3).
a(n) = 5*a(n-1)+2*a(n-2)+a(n-3) and a(0)=1, a(1)=4, a(2)=21. - Harvey P. Dale, Sep 18 2013
MATHEMATICA
Table[Sum[Binomial[3n - k + 1, 3n - 3k + 1], {k, 0, n}], {n, 0, 12}]
LinearRecurrence[{5, 2, 1}, {1, 4, 21}, 30] (* Harvey P. Dale, Sep 18 2013 *)
PROG
(Maxima) makelist(sum(binomial(3*n-k+1, 3*n-3*k+1), k, 0, n), n, 0, 24);
(PARI) Vec((1-x-x^2)/(1-5*x-2*x^2-x^3)+O(x^99)) \\ Charles R Greathouse IV, Jun 30 2011
(Magma) [(&+[Binomial(3*n-k+1, 3*n-3*k+1): k in [0..n]]): n in [0..30]]; // G. C. Greubel, Mar 04 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emanuele Munarini, May 04 2011
STATUS
approved