A128055 a(n) = 2^A128054(n).

1, 1, 2, 4, 8, 32, 64, 64, 128, 256, 512, 2048, 4096, 4096, 8192, 16384, 32768, 131072, 262144, 262144, 524288, 1048576, 2097152, 8388608, 16777216, 16777216, 33554432, 67108864, 134217728, 536870912, 1073741824

Offset: 0

Author

Paul Barry, Feb 13 2007

Keywords

• easy
• nonn

Comments

A factor in A128056.

The signed sequence 1,1,2,-4,-8,-32,-64,-64,-128,256,512... is the Hankel transform of the doubled sequence 1,1,2,2,6,6,... of central binomial coefficients (A128014). - Paul Barry, Sep 09 2008

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-4,8,-16,32).

Crossrefs

Cf. A128014, A128054, A128056.

Programs

Mathematica

LinearRecurrence[{2,-4,8,-16,32},{1,1,2,4,8},31] (* James C. McMahon, Jan 05 2025 *)

Formula

G.f.: (-1-16*x^4+4*x^3-4*x^2+x)/((2*x-1)*(4*x^2-2*x+1)*(4*x^2+2*x+1)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009

Sum_{n>=0} 1/a(n) = 62/21. - Amiram Eldar, Mar 28 2023