A363092 a(n) = 4*a(n-1) - 8*a(n-2) with a(0) = a(1) = 1.

1, 1, -4, -24, -64, -64, 256, 1536, 4096, 4096, -16384, -98304, -262144, -262144, 1048576, 6291456, 16777216, 16777216, -67108864, -402653184, -1073741824, -1073741824, 4294967296, 25769803776, 68719476736, 68719476736, -274877906944, -1649267441664, -4398046511104

Offset: 0

Author

Stefano Spezia, May 19 2023

Keywords

• sign
• easy

References

• Paul J. Nahin, An Imaginary Tale: The Story of sqrt(-1), Princeton University Press, Princeton, NJ. 1998, pp. 94-96.

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-8).

Crossrefs

Cf. A000045, A008586, A088137, A088138.

Programs

Mathematica

LinearRecurrence[{4,-8},{1,1},29]

Formula

a(n) = 2^(3*n/2-1)*(2*cos(n*Pi/4) - sin(n*Pi/4)).

O.g.f.: (1 - 3*x)/(1 - 4*x + 8*x^2).

E.g.f.: exp(2*x)*(2*cos(2*x) - sin(2*x))/2.

a(n+1) = a(n) iff n is a multiple of 4.