A114803 Integers when g2^3-27*g3^2=0 in cubic polynomials of the form: w^2=4*x^3-g2*x-g3.

1, 3, 8, 12, 27, 27, 64, 48, 125, 75, 216, 108, 343, 147, 512, 192, 729, 243, 1000, 300, 1331, 363, 1728, 432, 2197, 507, 2744, 588, 3375, 675, 4096, 768, 4913, 867

Offset

0,2

Comments

When the elliptic term: j=g2^3/(g2^3-27*g3^2) is singular and g2 and g3 are both integers.

Links

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (0,4,0,-6,0,4,0,-1).

Formula

a(n) = If 3*n^(2/3) is an integer then {n,3*n^(2/3)}

a(n) = (n^3+6*n^2+12*n+8)/8 for n even. a(n) = (3*n^2+6*n+3)/4 for n odd. G.f.: -(3*x^5-x^4-4*x^2-3*x-1) / ((x-1)^4*(x+1)^4). - Colin Barker, Mar 15 2013

Mathematica

a = Flatten[Table[If[IntegerQ[3*n^(2/3)] == True, {n, 3*n^(2/3)}, {}], {n, 1, 5000}]]

Crossrefs

Sequence in context: A326890 A024463 A092954 * A083171 A058582 A178720

Adjacent sequences: A114800 A114801 A114802 * A114804 A114805 A114806

Keyword

nonn,uned,easy

Author

Roger L. Bagula, Feb 18 2006

Status

approved