OFFSET
0,3
COMMENTS
Partial sums of the fourth powers of the terms of A000196.
LINKS
Karl-Heinz Hofmann, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = (n+1)*m^4 - (1/30)*m*(m+1)*(20*m^4+4*m^3-14*m^2+4*m+1), where m = floor(sqrt(n)).
MATHEMATICA
Table[(n + 1) #^4 - (1/30) # (# + 1)*(20 #^4 + 4 #^3 - 14 #^2 + 4 # + 1) &[Floor@ Sqrt[n]], {n, 0, 45}] (* Michael De Vlieger, Jun 10 2023 *)
PROG
(Python)
from math import isqrt
def A363498(n):
return (m:=isqrt(n))**4 *(n+1) - (m*(m+1)*(20*m**4+4*m**3-14*m**2+4*m+1))//30
print([A363498(n) for n in range(0, 46)]) # Karl-Heinz Hofmann, Jul 15 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Hans J. H. Tuenter, Jun 05 2023
STATUS
approved