OFFSET
0,2
COMMENTS
Let m=4. We observe that a(n) = Sum_{k=0..floor(n/2)} C(m,n-2*k). Then there is a link with A113311 and A040000: it is the same formula with respectively m=3 and m=2. We can generalize this result with the sequence whose G.f is given by (1+z)^(m-1)/(1-z). - Richard Choulet, Dec 08 2009
Also continued fraction expansion of (132-sqrt(17))/103. - Bruno Berselli, Sep 23 2011
Also decimal expansion of 1331/9000. - Vincenzo Librandi, Sep 23 2011
LINKS
FORMULA
a(n) = 8 - C(2, n) - 2*C(1, n) - 4*C(0, n).
a(n) = Sum_{k=0..n} C(3, k).
a(n) = A004070(n, 3).
From Elmo R. Oliveira, Aug 09 2024
E.g.f.: 8*exp(x) - 7 - 4*x - x^2/2.
a(n) = 8, n > 2. (End)
MATHEMATICA
CoefficientList[Series[(1+x)^3/(1-x), {x, 0, 100}], x] (* or *) PadRight[ {1, 4, 7}, 120, {8}] (* Harvey P. Dale, May 23 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Jan 19 2006
STATUS
approved