A016782 a(n) = (3*n+1)^6.

1, 4096, 117649, 1000000, 4826809, 16777216, 47045881, 113379904, 244140625, 481890304, 887503681, 1544804416, 2565726409, 4096000000, 6321363049, 9474296896, 13841287201, 19770609664, 27680640625, 38068692544, 51520374361, 68719476736, 90458382169, 117649000000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A001014, A016777, A016778, A016779, A016780, A016781.

Programs

Magma

[(3*n+1)^6: n in [0..30]]; // Vincenzo Librandi, Sep 21 2011

Mathematica

Table[(3n+1)^6,{n,0,100}] (* Mohammad K. Azarian, Jun 15 2016 *)
LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,4096,117649,1000000,4826809,16777216,47045881},20] (* Harvey P. Dale, Sep 30 2016 *)

Formula

a(n) = A001014(A016777(n)). - Michel Marcus, Jun 15 2016

From Ilya Gutkovskiy, Jun 15 2016: (Start)

G.f.: (1 + 4089*x + 88998*x^2 + 262438*x^3 + 154113*x^4 + 15177*x^5 + 64*x^6)/(1 - x)^7.

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). (End)

Sum_{n>=0} 1/a(n) = PolyGamma(5, 1/3)/87480. - Amiram Eldar, Mar 29 2022