A014833 - OEIS

%I #25 Sep 08 2022 08:44:39

%S 1,1,1,2,6,17,43,100,220,467,969,1982,4018,8101,16279,32648,65400,

%T 130919,261973,524098,1048366,2096921,4194051,8388332,16776916,

%U 33554107,67108513,134217350,268435050,536870477,1073741359,2147483152,4294966768,8589934031

%N a(n) = 2^n - n(n+1)/2.

%H Vincenzo Librandi, <a href="/A014833/b014833.txt">Table of n, a(n) for n = 0..240</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5, -9, 7, -2).

%F From _Harvey P. Dale_, May 12 2011: (Start)

%F a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4); a(0)=1, a(1)=1, a(2)=1, a(3)=2.

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

%F a(n) = A331105(n,n) for n>0. - _Alois P. Heinz_, Jan 16 2020

%p seq(2^n-n*(n+1)/2, n=0..30); # _Zerinvary Lajos_, Jul 01 2007

%t Table[2^n-n (n+1)/2,{n,0,50}] (* or *) LinearRecurrence[{5,-9,7,-2},{1,1,1,2},50] (* _Harvey P. Dale_, May 12 2011 *)

%o (Magma) [2^n - n*(n+1)/2: n in [0..50]]; // _Vincenzo Librandi_, Apr 25 2011

%Y Cf. A000079, A000217, A331105.

%K nonn

%O 0,4

%A _N. J. A. Sloane_