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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

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

Links

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

Crossrefs

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

Programs

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 *)

PARI

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

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

Extensions

Edited by T. D. Noe, Nov 12 2010