A016830 a(n) = (4*n+2)^6.

64, 46656, 1000000, 7529536, 34012224, 113379904, 308915776, 729000000, 1544804416, 3010936384, 5489031744, 9474296896, 15625000000, 24794911296, 38068692544, 56800235584, 82653950016, 117649000000, 164206490176, 225199600704, 304006671424, 404567235136, 531441000000

Offset

0,1

Links

Table of n, a(n) for n=0..22.

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

Formula

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7). - Harvey P. Dale, Oct 14 2012

From Amiram Eldar, Jul 07 2022: (Start)

a(n) = A016825(n)^6 = A016826(n)^3 = A016827(n)^2 = 64*A016758(n).

Sum_{n>=0} 1/a(n) = Pi^6/61440. (End)

Mathematica

(4*Range[0, 20]+2)^6 (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {64, 46656, 1000000, 7529536, 34012224, 113379904, 308915776}, 20] (* Harvey P. Dale, Oct 14 2012 *)

Crossrefs

Cf. A016758, A016825, A016826, A016827.

Sequence in context: A221615 A141092 A283924 * A249076 A334605 A103346

Adjacent sequences: A016827 A016828 A016829 * A016831 A016832 A016833

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved