A176712 - OEIS

%I #20 Sep 08 2022 08:45:53

%S 285,2805,9405,22197,43677,76725,124605,190965,279837,395637,543165,

%T 727605,954525,1229877,1559997,1951605,2411805,2948085,3568317,

%U 4280757,5094045,6017205,7059645,8231157,9541917,11002485,12623805,14417205

%N a(n) = 16*n^4 + 256*n^3 + 1160*n^2 + 1088*n + 285.

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

%H Vincenzo Librandi, <a href="/A176712/b176712.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*(95 + 460*x - 590*x^2 + 124*x^3 + 39*x^4)/(1-x)^5.

%F a(n) = (2*n+1)*(2*n+15)*(4*n^2+32*n+19).

%F a(n) = a(-n-8). - _Bruno Berselli_, Sep 05 2011

%t Table[16n^4+256n^3+1160n^2+1088n+285,{n,0,30}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{285,2805,9405,22197,43677},30] (* _Harvey P. Dale_, Jan 10 2017 *)

%o (Magma) [ 16*n^4+256*n^3+1160*n^2+1088*n+285: n in [0..27] ];

%Y Cf. A176711.

%K nonn,easy

%O 0,1

%A _Klaus Brockhaus_, Apr 24 2010