A016820 a(n) = (4*n + 1)^8.

1, 390625, 43046721, 815730721, 6975757441, 37822859361, 152587890625, 500246412961, 1406408618241, 3512479453921, 7984925229121, 16815125390625, 33232930569601, 62259690411361, 111429157112001, 191707312997281, 318644812890625, 513798374428641

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

Crossrefs

Cf. A001016, A016813, A016814.

Programs

Magma

[(4*n+1)^8: n in [0..20]]; // Vincenzo Librandi, Aug 28 2017

Maple

A016820:=n->(4*n+1)^8: seq(A016820(n), n=0..30); # Wesley Ivan Hurt, Jan 22 2017

Mathematica

(4 * Range[0, 20] + 1)^8 (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 390625, 43046721, 815730721, 6975757441, 37822859361, 152587890625, 500246412961, 1406408618241}, 20] (* Harvey P. Dale, Jul 11 2013 *)

Formula

a(0) = 1, a(1) = 390625, a(2) = 43046721, a(3) = 815730721, a(4) = 6975757441, a(5) = 37822859361, a(6) = 152587890625, a(7) = 500246412961, a(8) = 1406408618241, a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9). - Harvey P. Dale, Jul 11 2013

a(n) = A001016(A016813(n)). - Michel Marcus, Jan 23 2017