A152166 a(2*n) = 2^n; a(2*n+1) = -(2^(n+1)).

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

Offset: 0

Author

Philippe Deléham, Nov 27 2008

Keywords

• sign
• easy

Comments

Ratios of successive terms are -2,-1,-2,-1,-2,-1,-2,-1,... - Philippe Deléham, Dec 12 2008

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,2).

Crossrefs

Cf. A000079, A016116, A147703.

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

Programs

Mathematica

LinearRecurrence[{0, 2}, {1, -2}, 50] (* Paolo Xausa, Jul 19 2024 *)

Formula

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