A156561 Floor(Fibonacci(2n+1)/9).

0, 0, 0, 1, 3, 9, 25, 67, 177, 464, 1216, 3184, 8336, 21824, 57136, 149585, 391619, 1025273, 2684201, 7027331, 18397793, 48166048, 126100352, 330135008, 864304672, 2262779008, 5924032352, 15509318049, 40603921795, 106302447337, 278303420217

Offset: 0

Author

Paul Curtz, Feb 10 2009

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (4, -4, 1, 0, 0, -1, 4, -4, 1).

Crossrefs

Cf. A069403.

Programs

Mathematica

Floor[Fibonacci[2*Range[0,30]+1]/9] (* or *) LinearRecurrence[{4,-4,1,0,0,-1,4,-4,1},{0,0,0,1,3,9,25,67,177},31] (* Harvey P. Dale, Jun 06 2016 *)

Formula

a(n) = ( A000045(2n+1)-A154811(n) )/9 = floor(A122367(n)/9) = floor(A001519(n+1)/9) = floor( |A099496(n)|/9).

a(n)=3a(n-1)-a(n-2)+|A112690(n+10)|, i.e., a(n)-3a(n-1)+a(n-2) is a sequence of period 12 containing 0's and 1's. - R. J. Mathar, Feb 23 2009

G.f.: (1-x+x^2)/((1-x)(1+x^2)(1-3x+x^2)(1-x^2+x^4)). - R. J. Mathar, Feb 23 2009

Extensions

Edited and extended by R. J. Mathar, Jan 23 2009, Feb 23 2009