A016780 a(n) = (3*n+1)^4.

1, 256, 2401, 10000, 28561, 65536, 130321, 234256, 390625, 614656, 923521, 1336336, 1874161, 2560000, 3418801, 4477456, 5764801, 7311616, 9150625, 11316496, 13845841, 16777216, 20151121, 24010000, 28398241, 33362176, 38950081, 45212176, 52200625, 59969536, 68574961

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 (5,-10,10,-5,1).

Crossrefs

Cf. A000583 (n^4), A016777 (3n+1), A016778, A016779, A016781.

Programs

Magma

[(3*n+1)^4: n in [0..30]]; // Vincenzo Librandi, Sep 21 2011

Mathematica

(3*Range[0,30]+1)^4 (* or *) LinearRecurrence[{5,-10,10,-5,1},{1,256,2401,10000,28561},30] (* Harvey P. Dale, Oct 21 2015 *)

Formula

From Harvey P. Dale, Oct 21 2015: (Start)

a(n) = 5*a(n-1) -10*a(n-2) +10*a(n-3) -5*a(n-4) +a(n-5).

G.f.: -((1+251*x+1131*x^2+545*x^3+16*x^4)/(-1+x)^5). (End)

a(n) = A000583(A016777(n)). - Michel Marcus, Nov 06 2015

E.g.f.: exp(x)*(1+255*x+945*x^2+594*x^3+81*x^4). - Wolfdieter Lang, Apr 02 2017

Sum_{n>=0} 1/a(n) = PolyGamma(3, 1/3)/486. - Amiram Eldar, Mar 29 2022