A176711 a(n) = 16n^4 + 64n^3 + 104n^2 + 80n + 21.

21, 285, 1365, 4221, 10197, 21021, 38805, 66045, 105621, 160797, 235221, 332925, 458325, 616221, 811797, 1050621, 1338645, 1682205, 2088021, 2563197, 3115221, 3751965, 4481685, 5313021, 6254997, 7317021, 8508885, 9840765, 11323221

Offset

0,1

Comments

Since the formula can be factored, there are no primes in this sequence.

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) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + 384 for n > 3; a(0)=21, a(1)=285, a(2)=1365, a(3)=4221.

G.f.: 3*(7 + 60*x + 50*x^2 + 12*x^3 - x^4)/(1 - x)^5.

a(n) = (2*n + 1)*(2*n + 3)*(4*n^2 + 8*n + 7). - corrected by Eric Rowland, Aug 15 2017

a(n) = a(-n-2). - Bruno Berselli, Sep 05 2011

Mathematica

Table[16n^4+64n^3+104n^2+80n+21, {n, 0, 30}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {21, 285, 1365, 4221, 10197}, 30] (* Harvey P. Dale, Jan 15 2015 *)

Prog

(Magma) [ 16*n^4+64*n^3+104*n^2+80*n+21: n in [0..28] ];

Crossrefs

Cf. A176712.

Sequence in context: A223996 A323063 A028033 * A025987 A125456 A296333

Adjacent sequences: A176708 A176709 A176710 * A176712 A176713 A176714

Keyword

nonn,easy

Author

Klaus Brockhaus, Apr 24 2010

Status

approved