A219056 a(n) = 3*n^4.

0, 3, 48, 243, 768, 1875, 3888, 7203, 12288, 19683, 30000, 43923, 62208, 85683, 115248, 151875, 196608, 250563, 314928, 390963, 480000, 583443, 702768, 839523, 995328, 1171875, 1370928, 1594323, 1843968, 2121843, 2430000, 2770563, 3145728, 3557763, 4009008

Offset: 0

Author

Reinhard Zumkeller, Nov 11 2012

Keywords

• nonn
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A008585, A000583, A000290, A033428, A219069.

Programs

Haskell

a219056 = (* 3) . (^ 4)

Mathematica

LinearRecurrence[{5,-10,10,-5,1},{0, 3, 48, 243, 768},100] (* or *) Table[3*n^4, {n,0,50}] (* G. Greubel, Jun 22 2016 *)

Maxima

makelist(3*n^4,n,0,30); /* Martin Ettl, Nov 12 2012 */

PARI

a(n) = 3*n^4; \\ Michel Marcus, Jan 26 2022

Formula

a(n) = A219069(n,n) for n > 0;

a(n) = A008585(A000583(n)) = A000290(n)*A033428(n).

From Chai Wah Wu, Jun 22 2016: (Start)

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

G.f.: 3*x*(1 + x)*(1 + 10*x + x^2)/(1 - x)^5. (End)

E.g.f.: 3*x*(1 + 7*x + 6*x^2 + x^3)*exp(x). - G. C. Greubel, Jun 22 2016