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

0,2

Comments

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

Links

Table of n, a(n) for n=0..40.

Index entries for linear recurrences with constant coefficients, signature (0,2).

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

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

Sequence in context: A076939 A117575 A131572 * A320770 A016116 A060546

Adjacent sequences: A152163 A152164 A152165 * A152167 A152168 A152169

Keyword

sign,easy

Author

Philippe Deléham, Nov 27 2008

Status

approved