|
%I #25 Mar 19 2019 00:37:33
%S 2,3,4,9,18,39,80,165,334,675,1356,2721,5450,10911,21832,43677,87366,
%T 174747,349508,699033,1398082,2796183,5592384,11184789,22369598,
%U 44739219,89478460,178956945,357913914,715827855,1431655736
%N a(n) = 1 - n + (2^(n+2) - (-1)^n)/3.
%C a(n) mod 10 = period 20: repeat [2, 3, 4, 9, 8, 9, 0, 5, 4, 5, 6, 1, 0, 1, 2, 7, 6, 7, 8, 3] = disordered [0,0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9].
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-3,2).
%F a(n+1) - 2*(n) = -1, -2, 1, 0, 3, 2, 5, 4, ..., n >= 0.
%F a(n+1) - a(n) = A097074(n).
%F a(n+2) - 2*a(n+1) + a(n) = A097073(n+1).
%F From _Colin Barker_, Dec 26 2018: (Start)
%F G.f.: (2 - 3*x - 3*x^2 + 6*x^3) / ((1 - x)^2*(1 + x)*(1 - 2*x)).
%F a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + 2*a(n-4) for n > 3.
%F (End)
%o (PARI) Vec((2 - 3*x - 3*x^2 + 6*x^3) / ((1 - x)^2*(1 + x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, Dec 26 2018
%Y Cf. A001045, A004442(n-2), A097073, A097074.
%K nonn,easy
%O 0,1
%A _Paul Curtz_, Dec 26 2018
|
