A087887 a(n) = 18n^3 + 6n^2.

0, 24, 168, 540, 1248, 2400, 4104, 6468, 9600, 13608, 18600, 24684, 31968, 40560, 50568, 62100, 75264, 90168, 106920, 125628, 146400, 169344, 194568, 222180, 252288, 285000, 320424, 358668, 399840, 444048, 491400, 542004, 595968, 653400, 714408, 779100, 847584

Offset

0,2

Comments

Another parametric representation of the solutions of the Diophantine equation x^2 - y^2 = z^3 is (x,y,z) = (15n^3, 3n^3, 6n^2), thus getting a(n) = 18n^3 + 6n^2.

Links

Table of n, a(n) for n=0..36.

Formula

O.g.f.: 12x(2+6x+x^2)/(-1+x)^4. a(n) = 12*A036659(n). - R. J. Mathar, Apr 07 2008

From Amiram Eldar, Jan 10 2023: (Start)

Sum_{n>=1} 1/a(n) = Pi^2/36 + sqrt(3)*Pi/12 + 3*log(3)/4 - 3/2.

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/72 - sqrt(3)*Pi/6 - log(2) + 3/2. (End)

Mathematica

a[n_] := 18*n^3 + 6*n^2; Array[a, 50, 0] (* Amiram Eldar, Jan 10 2023 *)

Crossrefs

Cf. A036659, A085409, A085482.

Sequence in context: A250142 A019583 A244908 * A288486 A223291 A221069

Adjacent sequences: A087884 A087885 A087886 * A087888 A087889 A087890

Keyword

easy,nonn,changed

Author

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Oct 13 2003

Extensions

More terms from Ray Chandler, Nov 06 2003

Status

approved