cp's OEIS Frontend

A084174 a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + 2*a(n-4).

%I A084174 #24 Sep 08 2022 08:45:11
%S A084174 1,1,3,6,14,29,61,124,252,507,1019,2042,4090,8185,16377,32760,65528,
%T A084174 131063,262135,524278,1048566,2097141,4194293,8388596,16777204,
%U A084174 33554419,67108851,134217714,268435442,536870897,1073741809,2147483632
%N A084174 a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + 2*a(n-4).
%C A084174 Original name was: Generalized Jacobsthal numbers.
%C A084174 Row sums of triangle A131087. - _Gary W. Adamson_, Jun 14 2007
%H A084174 Vincenzo Librandi, <a href="/A084174/b084174.txt">Table of n, a(n) for n = 0..1000</a>
%H A084174 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-3,2).
%F A084174 a(n) = 2^n + (-1)^n/4 - (2*n+1)/4.
%F A084174 a(n+2) = a(n+1) + 2*a(n) + n, a(0)=1, a(1)=1.
%F A084174 a(n) = A084172(n) - A001045(n).
%F A084174 a(n) = floor(2^n - n*(n+1)/2). - _Zerinvary Lajos_, Apr 29 2007
%F A084174 G.f.: (1 - 2*x + x^2 + x^3)/(1 - 3*x + x^2 + 3*x^3 - 2*x^4). - _Colin Barker_, Jan 16 2012
%p A084174 seq(floor(2^n-n(n+1)/2),n=0..31); # _Zerinvary Lajos_, Apr 29 2007
%t A084174 LinearRecurrence[{3,-1,-3,2},{1,1,3,6},40] (* _Harvey P. Dale_, Feb 17 2021 *)
%o A084174 (Magma) [2^n+(-1)^n/4-(2*n+1)/4: n in [0..35]]; // _Vincenzo Librandi_, Jul 05 2011
%Y A084174 Cf. A131087.
%K A084174 nonn,easy
%O A084174 0,3
%A A084174 _Paul Barry_, May 18 2003