OFFSET
0,2
COMMENTS
The fractional portion of each sum converges to 3/10.
See A247112 for references to other related sequences and a conjecture.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = floor(Sum_{j=n^4+1..(n+1)^4-1} j^(1/4)).
a(n) = 3*n + 8*n^2 + 8*n^3 + 4*n^4.
G.f.: -x*(x^3+21*x^2+51*x+23) / (x-1)^5. - Colin Barker, Dec 30 2014
E.g.f.: exp(x)*x*(23 + 60*x + 32*x^2 + 4*x^3). - Stefano Spezia, Jul 13 2024
MATHEMATICA
Table[3 n + 8 n^2 + 8 n^3 + 4 n^4, {n, 0, 50}]
PROG
(PARI) a(n) = floor(sum(j=n^4+1, (n+1)^4-1, j^(1/4))); \\ Michel Marcus, Dec 22 2014
(PARI) concat(0, Vec(-x*(x^3+21*x^2+51*x+23)/(x-1)^5 + O(x^100))) \\ Colin Barker, Dec 30 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Richard R. Forberg, Dec 02 2014
STATUS
approved