A016912 a(n) = (6*n)^4.

0, 1296, 20736, 104976, 331776, 810000, 1679616, 3111696, 5308416, 8503056, 12960000, 18974736, 26873856, 37015056, 49787136, 65610000, 84934656, 108243216, 136048896, 168896016, 207360000, 252047376, 303595776, 362673936, 429981696, 506250000, 592240896, 688747536

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

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) with a(0)=0, a(1)=1296, a(2)=20736, a(3)=104976, a(4)=331776. - Harvey P. Dale, Mar 28 2015

From Elmo R. Oliveira, Nov 27 2025: (Start)

G.f.: 1296*x*(1 + x)*(1 + 10*x + x^2)/(1-x)^5.

E.g.f.: 1296*x*(1 + 7*x + 6*x^2 + x^3)*exp(x).

a(n) = 1296*A000583(n) = A016768(2*n) = A016744(3*n). (End)

Mathematica

(6*Range[0, 30])^4 (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1296, 20736, 104976, 331776}, 30] (* Harvey P. Dale, Mar 28 2015 *)

Prog

(Magma) [(6*n)^4: n in [0..40]]; // Vincenzo Librandi, May 03 2011

Crossrefs

Cf. A000583, A008588.

Cf. A016744, A016768, A016910, A016911.

Sequence in context: A016864 A064785 A223560 * A330980 A203820 A017056

Adjacent sequences: A016909 A016910 A016911 * A016913 A016914 A016915

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved