A133684 a(2n) = A001045(n); a(1)=1; a(2n+1) = 2*A001045(n-1) for n >= 1.

0, 1, 1, 0, 1, 2, 3, 2, 5, 6, 11, 10, 21, 22, 43, 42, 85, 86, 171, 170, 341, 342, 683, 682, 1365, 1366, 2731, 2730, 5461, 5462, 10923, 10922, 21845, 21846, 43691, 43690, 87381, 87382, 174763, 174762, 349525, 349526, 699051, 699050, 1398101, 1398102, 2796203, 2796202

Offset: 0

Author

Paul Curtz, Jan 04 2008

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,1,0,2).

Crossrefs

Cf. A001045, A016116, A133730 (first differences).

Programs

PARI

a(n)=([0,1,0,0; 0,0,1,0; 0,0,0,1; 2,0,1,0]^n*[0;1;1;0])[1,1] \\ Charles R Greathouse IV, Oct 03 2016

Formula

a(4*n) + a(4*n+1) = a(4*n+2).

a(n) + a(n+2) = 2^floor(n/2) = A016116(n).

O.g.f.: x - x^2*(1 + 2*x^3)/((2*x^2-1)*(x^2+1)) . - R. J. Mathar, Feb 23 2008

a(n+1) = 2*A135318(n) - A135318(n+1). - Paul Curtz, May 27 2024

Extensions

Terms a(24) and beyond from Andrew Howroyd, Feb 02 2020