A185270 a(n) = 648 * n^6.

0, 648, 41472, 472392, 2654208, 10125000, 30233088, 76236552, 169869312, 344373768, 648000000, 1147971528, 1934917632, 3127772232, 4879139328, 7381125000, 10871635968, 15641144712, 22039921152, 30485730888, 41472000000, 55576446408, 73470177792, 95927256072

Offset

0,2

Comments

Numbers n such that n/2 is a square and n/3 is a cube.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

a(n) = 648*n^6 = 648*A001014(n).

G.f.: -648*x*(x+1)*(x^4+56*x^3+246*x^2+56*x+1) / (x-1)^7.

Example

41472 is a member since 41472/2 = 20736 = 144^2 and 41472/3 = 13824 = 24^3.

Mathematica

Table[648*n^6, {n, 0, 23}] (* Zak Seidov, Jun 11 2015 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 648, 41472, 472392, 2654208, 10125000, 30233088}, 30] (* Harvey P. Dale, Mar 31 2016 *)

Prog

(PARI) a(n)=648*n^6 \\ Charles R Greathouse IV, Jun 11 2015

Crossrefs

Cf. A000290, A000578, A001014.

Sequence in context: A165611 A282334 A034619 * A250343 A035755 A107551

Adjacent sequences: A185267 A185268 A185269 * A185271 A185272 A185273

Keyword

nonn,easy

Author

Jayanta Basu, Apr 23 2013

Status

approved