A086822 - OEIS

%I #9 Apr 22 2018 12:25:22

%S 6,8,10,13,16,19,22,25,28,31,34,37,40,43,46,49,52,55,58,61,64,67,70,

%T 73,76,79,82,85,88,91,94,97,100,103,106,109,112,115,118,121,124,127,

%U 130,133,136,139,142,145,148,151,154,157,160,163,166,169,172,175

%N a(n) = floor((6*n^0+5*n^1+4*n^2+3*n^3) / (1*n^0+1*n^1+1*n^2)).

%H Colin Barker, <a href="/A086822/b086822.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = floor(3n+1+(5+n)/(1+n+n^2)) = 3n+1 = A112414(n-2) for n>2. - _R. J. Mathar_, Dec 13 2008

%F a(n) = 2*a(n-1)-a(n-2) for n>4. - _Colin Barker_, May 23 2015

%F G.f.: x*(x^3-4*x+6) / (x-1)^2. - _Colin Barker_, May 23 2015

%e a(3) = floor((6*3^0+5*3^1+4*3^2+3*3^3)/(1*3^0+1*3^1+1*3^2)) = floor(138/13) = floor(10.615) = 10.

%t Table[Floor[(6+5n+4n^2+3n^3)/(1+n+n^2)],{n,60}] (* _Harvey P. Dale_, Apr 22 2018 *)

%o (PARI) Vec(x*(x^3-4*x+6)/(x-1)^2 + O(x^100)) \\ _Colin Barker_, May 23 2015

%Y Cf. A086790, A086814.

%K easy,nonn

%O 1,1

%A Wang Dan (wangdan01(AT)lycos.com), Aug 07 2003