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a(0) = 3, a(n+1) = 2*a(n) + periodic sequence of length 2: repeat [-5, 4].
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%I #18 Nov 13 2023 08:44:17

%S 3,1,6,7,18,31,66,127,258,511,1026,2047,4098,8191,16386,32767,65538,

%T 131071,262146,524287,1048578,2097151,4194306,8388607,16777218,

%U 33554431,67108866,134217727,268435458,536870911,1073741826,2147483647,4294967298,8589934591

%N a(0) = 3, a(n+1) = 2*a(n) + periodic sequence of length 2: repeat [-5, 4].

%C From 1, the last digit is a periodic sequence of length 4:repeat [1, 6, 7, 8].

%H Colin Barker, <a href="/A280293/b280293.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2).

%F a(2n) = 4^n + 2. a(2n+1) = 2*4^n - 1.

%F a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3), n>2.

%F a(n) = 2^n + periodic sequence of length 2: repeat [2, -1].

%F a(n) = 2^(n+2) - A280173(n).

%F a(n+2) = a(n) + 3*2^n, a(0) = 3, a(1) = 1.

%F G.f.: (3-5*x+x^2) / ((1-x)*(1+x)*(1-2*x)). - _Colin Barker_, Dec 31 2016

%t LinearRecurrence[{2,1,-2},{3,1,6},50] (* _Paolo Xausa_, Nov 13 2023 *)

%o (PARI) Vec((3-5*x+x^2) / ((1-x)*(1+x)*(1-2*x)) + O(x^40)) \\ _Colin Barker_, Dec 31 2016

%Y Cf. A007283, A083420, A178789, A280173.

%K nonn,easy

%O 0,1

%A _Paul Curtz_, Dec 31 2016

%E More terms from _Colin Barker_, Dec 31 2016