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%I #40 Jan 13 2019 08:49:01
%S 4,11,19,41,79,161,319,641,1279,2561,5119,10241,20479,40961,81919,
%T 163841,327679,655361,1310719,2621441,5242879,10485761,20971519,
%U 41943041,83886079,167772161,335544319,671088641
%N a(n) = 5*2^n - (-1)^n.
%H Colin Barker, <a href="/A321643/b321643.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,2).
%F a(n+2) - a(n) = a(n+1) + a(n) = 15*2^n, n >= 0.
%F a(n) - 2*a(n-1) = period 2: repeat [3, -3], n > 0, a(0)=4, a(1)=11.
%F a(n+1) = 10*A051049(n) + period 2: repeat [1, 9].
%F a(n) = 12*2^n - A321483(n), n >= 0.
%F a(n) = 2^(n+2) + 3*A001045(n), n >= 0.
%F a(n) == A070366(n+4) (mod 9).
%F From _Colin Barker_, Dec 04 2018: (Start)
%F G.f.: (4 + 7*x) / ((1 + x)*(1 - 2*x)).
%F a(n) = a(n-1) + 2*a(n-2) for n > 1.
%F (End)
%p [5*2^n-(-1)^n$n=0..30]; # _Muniru A Asiru_, Dec 05 2018
%t a[n_] := 5*2^n - (-1)^n; Array[a, 30, 0] (* _Amiram Eldar_, Dec 03 2018 *)
%o (PARI) Vec((4 + 7*x) / ((1 + x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, Dec 04 2018
%o (GAP) List([0..30],n->5*2^n-(-1)^n); # _Muniru A Asiru_, Dec 05 2018
%o (Python) for n in range(0,30): print(5*2**n - (-1)**n) # _Stefano Spezia_, Dec 05 2018
%Y Cf. A020714, A010690, A010701, A051049, A070366, A110286.
%Y Cf. A001045, A081808, A321483.
%K nonn,easy
%O 0,1
%A _Paul Curtz_, Dec 03 2018
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