OFFSET
1,1
COMMENTS
7 and 41 are the only primes in the sequence.
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = ceiling(1/f(n))/2, where f(n) = (n + 1/(3*n)) - (n^3 + n)^(1/3), n > 0.
Note that (n^3 + n)^(1/3) converges to n + 1/(3*n) as n -> infinity. Therefore f(n) is the residual.
From Colin Barker, Apr 01 2014: (Start)
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
G.f.: x*(7*x^2 + 13*x + 7) / (x-1)^4. (End)
PROG
(PARI) Vec(x*(7*x^2+13*x+7)/(x-1)^4 + O(x^100)) \\ Colin Barker, Apr 01 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Richard R. Forberg, Feb 22 2014
EXTENSIONS
More terms from Colin Barker, Apr 01 2014
STATUS
approved