A029745 Expansion of (1 + 2x + 6x^2 + x^3)/(1 - 2x^2).

1, 2, 8, 5, 16, 10, 32, 20, 64, 40, 128, 80, 256, 160, 512, 320, 1024, 640, 2048, 1280, 4096, 2560, 8192, 5120, 16384, 10240, 32768, 20480, 65536, 40960, 131072, 81920, 262144, 163840, 524288, 327680, 1048576, 655360, 2097152, 1310720, 4194304

Offset

1,2

Comments

Note that 4 is the only power of 2 not here. All terms are either 2^k or 5*2^k.

Links

Table of n, a(n) for n=1..41.

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

Formula

G.f.: (1 + 2x + 6x^2 + x^3)/(1 - 2x^2).

Sum_{n>=1} 1/a(n) = 43/20. - Amiram Eldar, Jan 21 2022

Mathematica

LinearRecurrence[{0, 2}, {1, 2, 8, 5}, 50] (* or *) With[{nn=20}, Join[{1, 2}, Riffle[ 8*2^Range[0, nn], 5 2^Range[0, nn]]]] (* Harvey P. Dale, Sep 28 2016 *)

Prog

(PARI) a(n)=if(n<2, 1+max(-1, n), 2^(n\2)*if(n%2, 5/2, 4))

Crossrefs

Cf. A094958 (numbers of the form 2^k or 5*2^k).

Sequence in context: A309792 A318725 A155901 * A332067 A183232 A344691

Adjacent sequences: A029742 A029743 A029744 * A029746 A029747 A029748

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Edited by T. D. Noe, Nov 12 2010

Status

approved