A082645 - OEIS

%I #27 Jan 02 2023 13:27:12

%S -1,-1,1,4,8,12,18,25,33,41,51,62,74,86,100,115,131,147,165,184,204,

%T 224,246,269,293,317,343,370,398,426,456,487,519,551,585,620,656,692,

%U 730,769,809,849,891,934,978,1022,1068,1115,1163,1211,1261,1312,1364,1416,1470,1525

%N a(n) = floor((2*n^2 + n - 4)/4).

%H Colin Barker, <a href="/A082645/b082645.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,1,-2,1).

%F From _Colin Barker_, Jul 23 2017: (Start)

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

%F a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*a(n-5) + a(n-6) for n>5.

%F (End)

%p A082645:=n->floor((2*n^2+n-4)/4): seq(A082645(n), n=0..100); # _Wesley Ivan Hurt_, Jul 23 2017

%t Table[Floor[(2 n^2 + n - 4)/4], {n, 0, 55}] (* _Michael De Vlieger_, Jul 22 2017 *)

%t LinearRecurrence[{2,-1,0,1,-2,1},{-1,-1,1,4,8,12},60] (* _Harvey P. Dale_, Jan 02 2023 *)

%o (PARI) a(n) = (2*n^2 + n - 4)\4; \\ _Michel Marcus_, Jul 23 2017

%o (PARI) Vec(-(1 - x - 2*x^2 - x^3 - 2*x^4 + x^5) / ((1 - x)^3*(1 + x)*(1 + x^2)) + O(x^100)) \\ _Colin Barker_, Jul 23 2017

%K sign,easy

%O 0,4

%A _N. J. A. Sloane_, May 16 2003