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 A363092 a(n) = 4*a(n-1) - 8*a(n-2) with a(0) = a(1) = 1. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES Paul J. Nahin, An Imaginary Tale: The Story of sqrt(-1), Princeton University Press, Princeton, NJ. 1998, pp. 94-96. LINKS Table of n, a(n) for n=0..28. Index entries for linear recurrences with constant coefficients, signature (4,-8). 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. MATHEMATICA LinearRecurrence[{4, -8}, {1, 1}, 29] CROSSREFS Cf. A000045, A008586, A088137, A088138. Sequence in context: A166870 A124350 A112611 * A212066 A336039 A364600 Adjacent sequences: A363089 A363090 A363091 * A363093 A363094 A363095 KEYWORD sign,easy AUTHOR Stefano Spezia, May 19 2023 STATUS approved

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Last modified February 22 22:43 EST 2024. Contains 370265 sequences. (Running on oeis4.)