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A152166
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a(2*n) = 2^n; a(2*n+1) = -(2^(n+1)).
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25
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1, -2, 2, -4, 4, -8, 8, -16, 16, -32, 32, -64, 64, -128, 128, -256, 256, -512, 512, -1024, 1024, -2048, 2048, -4096, 4096, -8192, 8192, -16384, 16384, -32768, 32768, -65536, 65536, -131072, 131072, -262144, 262144, -524288, 524288, -1048576, 1048576
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OFFSET
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0,2
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COMMENTS
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Ratios of successive terms are -2,-1,-2,-1,-2,-1,-2,-1,... - Philippe Deléham, Dec 12 2008
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LINKS
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FORMULA
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G.f.: (1 - 2*x)/(1 - 2*x^2).
a(n) = 2*a(n-2); a(0)=1, a(1)=-2.
a(n) = Sum_{k=0..n} A147703(n,k)*(-3)^k.
E.g.f.: cosh(sqrt(2)*x) - sqrt(2)*sinh(sqrt(2)*x). - Stefano Spezia, Feb 05 2023
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MATHEMATICA
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LinearRecurrence[{0, 2}, {1, -2}, 50] (* Paolo Xausa, Jul 19 2024 *)
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CROSSREFS
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The following sequences are all essentially the same, in the sense that they are simple transformations of each other, with A029744 = {s(n), n>=1}, the numbers 2^k and 3*2^k, as the parent: A029744 (s(n)); A052955 (s(n)-1), A027383 (s(n)-2), A354788 (s(n)-3), A347789 (s(n)-4), A209721 (s(n)+1), A209722 (s(n)+2), A343177 (s(n)+3), A209723 (s(n)+4); A060482, A136252 (minor differences from A354788 at the start); A354785 (3*s(n)), A354789 (3*s(n)-7). The first differences of A029744 are 1,1,1,2,2,4,4,8,8,... which essentially matches eight sequences: A016116, A060546, A117575, A131572, A152166, A158780, A163403, A320770. The bisections of A029744 are A000079 and A007283. - N. J. A. Sloane, Jul 14 2022
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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