A155138 a(n) = nonnegative value y such that (A155136(n), y) is a solution to the Diophantine equation x^3+28*x^2 = y^2.

0, 27, 48, 57, 48, 15, 48, 147, 288, 477, 720, 1023, 1392, 1833, 2352, 2955, 3648, 4437, 5328, 6327, 7440, 8673, 10032, 11523, 13152, 14925, 16848, 18927, 21168, 23577, 26160, 28923, 31872, 35013, 38352, 41895, 45648, 49617, 53808, 58227, 62880

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..41.

Formula

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

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.

Example

(A155136(4), a(4)) = (-19, 57) is a solution: (-19)^3+28*(-19)^2 = -6859+10108 = 3249 = 57^2.
(A155136(8), a(8)) = (21, 147) is a solution: 21^3+28*21^2 = 9261+12348 = 21609 = 147^2.

Mathematica

Abs[#^3-28#]&/@Range[0, 40] (* Harvey P. Dale, Aug 30 2016 *)

Prog

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

Crossrefs

Cf. A155136, A155137, A153642.

Sequence in context: A153260 A254209 A155137 * A031325 A090761 A090760

Adjacent sequences: A155135 A155136 A155137 * A155139 A155140 A155141

Keyword

nonn

Author

Klaus Brockhaus, Jan 21 2009

Status

approved