cp's OEIS Frontend

A248698 Floor of sums of the non-integer fourth roots of n, as partitioned by the integer roots: floor(Sum_{j=n^4+1..(n+1)^4-1} j^(1/4)).

%I A248698 #40 Jul 14 2024 08:50:18
%S A248698 0,23,166,621,1676,3715,7218,12761,21016,32751,48830,70213,97956,
%T A248698 133211,177226,231345,297008,375751,469206,579101,707260,855603,
%U A248698 1026146,1221001,1442376,1692575,1973998,2289141,2640596,3031051,3463290,3940193,4464736,5039991
%N A248698 Floor of sums of the non-integer fourth roots of n, as partitioned by the integer roots: floor(Sum_{j=n^4+1..(n+1)^4-1} j^(1/4)).
%C A248698 The fractional portion of each sum converges to 3/10.
%C A248698 See A247112 for references to other related sequences and a conjecture.
%H A248698 Colin Barker, <a href="/A248698/b248698.txt">Table of n, a(n) for n = 0..1000</a>
%H A248698 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A248698 a(n) = floor(Sum_{j=n^4+1..(n+1)^4-1} j^(1/4)).
%F A248698 a(n) = 3*n + 8*n^2 + 8*n^3 + 4*n^4.
%F A248698 G.f.: -x*(x^3+21*x^2+51*x+23) / (x-1)^5. - _Colin Barker_, Dec 30 2014
%F A248698 E.g.f.: exp(x)*x*(23 + 60*x + 32*x^2 + 4*x^3). - _Stefano Spezia_, Jul 13 2024
%t A248698 Table[3 n + 8 n^2 + 8 n^3 + 4 n^4, {n, 0, 50}]
%o A248698 (PARI) a(n) = floor(sum(j=n^4+1, (n+1)^4-1, j^(1/4))); \\ _Michel Marcus_, Dec 22 2014
%o A248698 (PARI) concat(0, Vec(-x*(x^3+21*x^2+51*x+23)/(x-1)^5 + O(x^100))) \\ _Colin Barker_, Dec 30 2014
%Y A248698 Cf. A247112, A248575, A248621.
%K A248698 nonn,easy
%O A248698 0,2
%A A248698 _Richard R. Forberg_, Dec 02 2014