OFFSET
3,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 3..1000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
From Johannes W. Meijer, Nov 23 2009: (Start)
a(n) = (7*n^5 - 30*n^4 + 45*n^3 - 30*n^2 + 8*n)/5!.
G.f.: (1*z^2 + 4*z + 2)/(1-z)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).
a(n) - 5*a(n-1) + 10*a(n-2) - 10*a(n-3) + 5*a(n-4) - a(n-5) = 7. (End)
MATHEMATICA
Table[(7*n^5 - 30*n^4 + 45*n^3 - 30*n^2 + 8*n)/5!, {n, 3, 100}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {2, 16, 67, 202, 497, 1064}, 100] (* G. C. Greubel, Jun 16 2016 *)
PROG
(PARI) Vec((1*z^2 + 4*z + 2)/(1-z)^6 + O(z^50)) \\ Michel Marcus, Jul 05 2017
(PARI) a(n) = n*(7*n^4 - 30*n^3 + 45*n^2 - 30*n + 8)/120 \\ Charles R Greathouse IV, Jul 14 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Johannes W. Meijer, Nov 10 2009
STATUS
approved