A155138 - OEIS

%I #5 Sep 08 2022 08:45:40

%S 0,27,48,57,48,15,48,147,288,477,720,1023,1392,1833,2352,2955,3648,

%T 4437,5328,6327,7440,8673,10032,11523,13152,14925,16848,18927,21168,

%U 23577,26160,28923,31872,35013,38352,41895,45648,49617,53808,58227,62880

%N a(n) = nonnegative value y such that (A155136(n), y) is a solution to the Diophantine equation x^3+28*x^2 = y^2.

%C Agrees with A155137 except for omission of zero after a(6) = 15.

%F a(n) = Abs((n-1)^3-28*(n-1)).

%F G.f.: 3*x*(9-20*x+9*x^2+32*x^5-30*x^6-8*x^7+10*x^8)/(1-x)^4.

%e (A155136(4), a(4)) = (-19, 57) is a solution: (-19)^3+28*(-19)^2 = -6859+10108 = 3249 = 57^2.

%e (A155136(8), a(8)) = (21, 147) is a solution: 21^3+28*21^2 = 9261+12348 = 21609 = 147^2.

%t Abs[#^3-28#]&/@Range[0,40] (* _Harvey P. Dale_, Aug 30 2016 *)

%o (Magma) [ Abs((n-1)^3-28*(n-1)): n in [1..41] ];

%Y Cf. A155136, A155137, A153642.

%K nonn

%O 1,2

%A _Klaus Brockhaus_, Jan 21 2009