A176711 - OEIS

%I #23 Sep 08 2022 08:45:53

%S 21,285,1365,4221,10197,21021,38805,66045,105621,160797,235221,332925,

%T 458325,616221,811797,1050621,1338645,1682205,2088021,2563197,3115221,

%U 3751965,4481685,5313021,6254997,7317021,8508885,9840765,11323221

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

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

%H Vincenzo Librandi, <a href="/A176711/b176711.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F 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.

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

%F a(n) = (2*n + 1)*(2*n + 3)*(4*n^2 + 8*n + 7). - corrected by _Eric Rowland_, Aug 15 2017

%F a(n) = a(-n-2). - _Bruno Berselli_, Sep 05 2011

%t 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 *)

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

%Y Cf. A176712.

%K nonn,easy

%O 0,1

%A _Klaus Brockhaus_, Apr 24 2010