A016984 a(n) = (7*n)^4.

0, 2401, 38416, 194481, 614656, 1500625, 3111696, 5764801, 9834496, 15752961, 24010000, 35153041, 49787136, 68574961, 92236816, 121550625, 157351936, 200533921, 252047376, 312900721, 384160000, 466948881, 562448656, 671898241, 796594176, 937890625, 1097199376

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5); a(0)=0, a(1)=2401, a(2)=38416, a(3)=194481, a(4)=614656. - Harvey P. Dale, Mar 05 2013

From Elmo R. Oliveira, Nov 28 2025: (Start)

a(n) = 2401*A000583(n).

E.g.f.: 2401*x*(1 + 7*x + 6*x^2 + x^3)*exp(x).

G.f.: 2401*x*(1 + x)*(1 + 10*x + x^2)/(1 - x)^5. (End)

Mathematica

(7*Range[0, 20])^4 (* Harvey P. Dale, Mar 05 2013 *)
(* Alternative: *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 2401, 38416, 194481, 614656}, 30] (* Harvey P. Dale, Mar 05 2013 *)

Prog

(Magma) [(7*n)^4: n in [0..30]]; // Vincenzo Librandi, May 23 2011

Crossrefs

Cf. A000583.

Sequence in context: A103125 A074384 A016924 * A017152 A017248 A017356

Adjacent sequences: A016981 A016982 A016983 * A016985 A016986 A016987

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved