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%I #18 Sep 08 2022 08:46:13
%S 3213,3950,4807,5796,6929,8218,9675,11312,13141,15174,17423,19900,
%T 22617,25586,28819,32328,36125,40222,44631,49364,54433,59850,65627,
%U 71776,78309,85238,92575,100332,108521,117154,126243,135800,145837,156366
%N One half of numbers representable in at least two different ways as sums of four nonvanishing cubes. See A259060 for these numbers and their representations.
%C See A259060. There may be other numbers with this property.
%D W. Sierpiński, 250 Problems in Elementary Number Theory, American Elsevier Publ. Comp., New York, PWN-Polish Scientific Publishers, Warszawa, 1970, Problem 227, p. 20 and p. 110.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = (n+9)*(2*n^2 + 36*n + 357), n >= 0.
%F O.g.f.: (3213 - 8902*x + 8285*x^2 - 2584*x^3)/(1-x)^4.
%F a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - _Vincenzo Librandi_, Aug 13 2015
%t CoefficientList[Series[(3213 - 8902 x + 8285 x^2 - 2584 x^3)/(1 - x)^4, {x, 0, 50}], x] (* _Vincenzo Librandi_, Aug 13 2015 *)
%o (Magma) [(n+9)*(2*n^2 + 36*n + 357): n in [0..50]] /* or */ I:=[3213,3950,4807,5796]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // _Vincenzo Librandi_, Aug 13 2015
%Y Cf. A259060.
%K nonn,easy
%O 0,1
%A _Wolfdieter Lang_, Aug 12 2015
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