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%I #34 Jun 13 2015 00:55:16
%S 0,23,166,621,1676,3715,7218,12761,21016,32751,48830,70213,97956,
%T 133211,177226,231345,297008,375751,469206,579101,707260,855603,
%U 1026146,1221001,1442376,1692575,1973998,2289141,2640596,3031051,3463290,3940193,4464736,5039991
%N Floor of sums of the non-integer fourth roots of n, as partitioned by the integer roots: floor[sum(j from n^4+1 to (n+1)^4-1, j^(1/4))].
%C The fractional portion of each sum converges to 3/10.
%C See A247112 for references to other related sequences and a conjecture.
%H Colin Barker, <a href="/A248698/b248698.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = floor[sum(j from n^4+1 to (n+1)^4-1, j^(1/4))].
%F a(n) = 3*n + 8*n^2 + 8*n^3 + 4*n^4.
%F G.f.: -x*(x^3+21*x^2+51*x+23) / (x-1)^5. - _Colin Barker_, Dec 30 2014
%t Table[AccountingForm[N[Sum[j^(1/4), {j, n^4 + 1, (n + 1)^4 - 1}], 20]], {n, 0, 50}]
%t Table[3 n + 8 n^2 + 8 n^3 + 4 n^4, {n, 0, 50}]
%o (PARI) a(n) = floor(sum(j=n^4+1, (n+1)^4-1, j^(1/4))); \\ _Michel Marcus_, Dec 22 2014
%o (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 Cf. A247112.
%K nonn,easy
%O 0,2
%A _Richard R. Forberg_, Dec 02 2014
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