A343085 - OEIS

%I #12 Aug 06 2022 14:21:17

%S 13896,1979,1252,626,470,256,224,225,226,227,221,222,223,203,204,205,

%T 171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,

%U 188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205

%N a(n) is the smallest number that is the sum of n positive cubes in four ways.

%C This is r(n,3,4) in Alter's notation.

%H R. Alter, <a href="https://doi.org/10.1007/BFb0096461">Computations and generalizations on a remark of Ramanujan</a>, pp. 182-196 of "Analytic Number Theory (Philadelphia, 1980)", ed. M. I. Knopp, Lect. Notes Math., Vol. 899, 1981. See Table 11, page 194.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = n + 152 for n >= 19.

%e a(3) = 13896 = 1^3 + 12^3 + 23^3 = 2^3 + 4^3 + 24^3 = 4^3 + 18^3 + 20^3 = 9^3 + 10^3 + 23^3.

%e a(4) = 1979 = 1^3 + 5^3 + 5^3 + 12^3 = 2^3 + 3^3 + 6^3 + 12^3 = 5^3 + 5^3 + 9^3 + 10^3 = 6^3 + 6^3 + 6^3 + 11^3.

%t LinearRecurrence[{2,-1},{13896,1979,1252,626,470,256,224,225,226,227,221,222,223,203,204,205,171,172},60] (* _Harvey P. Dale_, Aug 06 2022 *)

%Y Cf. A342902, A343081, A343084, A343086.

%K nonn

%O 3,1

%A _Sean A. Irvine_, Apr 04 2021