A190966 a(n) = 4*a(n-1) - 8*a(n-2), with a(0)=0, a(1)=1.
0, 1, 4, 8, 0, -64, -256, -512, 0, 4096, 16384, 32768, 0, -262144, -1048576, -2097152, 0, 16777216, 67108864, 134217728, 0, -1073741824, -4294967296, -8589934592, 0, 68719476736, 274877906944, 549755813888, 0, -4398046511104, -17592186044416, -35184372088832
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-8).
Crossrefs
Cf. A190958 (index to generalized Fibonacci sequences).
Programs
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Magma
[n le 2 select n-1 else 4*(Self(n-1) -2*Self(n-2)): n in [1..41]]; // G. C. Greubel, Jan 10 2024
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Mathematica
LinearRecurrence[{4,-8}, {0,1}, 50] -
SageMath
A190966=BinaryRecurrenceSequence(4,-8,0,1) [A190966(n) for n in range(41)] # G. C. Greubel, Jan 10 2024
Formula
G.f.: x/(1 - 4*x + 8*x^2). - Philippe Deléham, Oct 12 2011
a(n) = 2^(n-1)*A009545(n). - R. J. Mathar, Apr 07 2022
From G. C. Greubel, Jan 10 2024: (Start)
a(n) = 8^((n-1)/2)*ChebyshevU(n-1, 1/sqrt(2)).
E.g.f.: (1/2)*exp(2*x)*sin(2*x). (End)
a(n) = (i/4)*((2 - 2*i)^n - (2 + 2*i)^n), where i=sqrt(-1). - Taras Goy, Jan 04 2025