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 A275060 Numbers n such that there exists x in N : (x+1)^3 - x^3 = 61*n^2. 2

%I #12 Jul 15 2016 12:59:39

%S 1,973,947701,923059801,899059298473,875682833652901,

%T 852914180918627101,830737536531909143473,809137507667898587115601,

%U 788099101730996691941451901,767607715948483110052387035973,747649127234720818194333031585801

%N Numbers n such that there exists x in N : (x+1)^3 - x^3 = 61*n^2.

%H Colin Barker, <a href="/A275060/b275060.txt">Table of n, a(n) for n = 1..300</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (974,-1).

%F G.f.: x*(1-x) / (1-974*x+x^2).

%F a(n) = 974*a(n-1) - a(n-2) for n>2.

%F a(n) = ((487 + 36*sqrt(183))^(-n)*(2 - 9*sqrt(3/61) + (2+9*sqrt(3/61))* (487 + 36*sqrt(183))^(2*n)))/4.

%e 973 is in the sequence because 973^2 = 946729 = ((4387+1)^3-4387^3)/61.

%t LinearRecurrence[{974,-1},{1,973}, 50] (* _G. C. Greubel_, Jul 15 2016 *)

%o (PARI) Vec(x*(1-x)/(1-974*x+x^2) + O(x^20))

%Y Cf. A274972.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Jul 15 2016

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Last modified August 13 10:15 EDT 2024. Contains 375130 sequences. (Running on oeis4.)