This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A363498 #31 Jul 20 2023 20:17:09 %S A363498 0,1,2,3,19,35,51,67,83,164,245,326,407,488,569,650,906,1162,1418, %T A363498 1674,1930,2186,2442,2698,2954,3579,4204,4829,5454,6079,6704,7329, %U A363498 7954,8579,9204,9829,11125,12421,13717,15013,16309,17605,18901,20197,21493,22789 %N A363498 a(n) = Sum_{k=0..n} floor(sqrt(k))^4. %C A363498 Partial sums of the fourth powers of the terms of A000196. %H A363498 Karl-Heinz Hofmann, <a href="/A363498/b363498.txt">Table of n, a(n) for n = 0..10000</a> %F A363498 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)). %t A363498 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 *) %o A363498 (Python) %o A363498 from math import isqrt %o A363498 def A363498(n): %o A363498 return (m:=isqrt(n))**4 *(n+1) - (m*(m+1)*(20*m**4+4*m**3-14*m**2+4*m+1))//30 %o A363498 print([A363498(n) for n in range(0,46)]) # _Karl-Heinz Hofmann_, Jul 15 2023 %Y A363498 Sums of powers of A000196: A022554 (1st), A174060 (2nd), A363497 (3rd), this sequence (4th), A363499 (5th). %K A363498 nonn,easy %O A363498 0,3 %A A363498 _Hans J. H. Tuenter_, Jun 05 2023