OFFSET
1,4
COMMENTS
Also A266535 and twice the terms of A256249 interleaved, or in other words A266535 and A266538 interleaved.
It appears that this sequence has a fractal (or fractal-like) behavior.
For an illustration of initial terms consider the diagram of A256249 in the fourth quadrant of the square grid together with a reflected copy in the second quadrant.
Also the third sequence of Betti numbers of the Lie algebra m_0(n) over Z_2. See the Nikolayevsky-Tsartsaflis paper, pages 2 and 6. Note that a(n) is denoted by b_3(m_0(n)).
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Yuri Nikolayevsky and Ioannis Tsartsaflis, Cohomology of N-graded Lie algebras of maximal class over Z_2, arXiv:1512.87676 [math.RA], (2016); see pp. 2 and 6.
FORMULA
a(2n-1) = A266535(n).
a(n) = (a(n-1) + a(n+1))/2, if n is an odd number greater than 1.
G.f.: (x^3+x^5)/(1-2*x+2*x^3-x^4) - x*(1-x)^(-2)*Sum_{k>=1} 2^k*x^(2^(1+k)). - Robert Israel, Jan 13 2016
MAPLE
ListTools:-PartialSums([seq(A006257[i]$2, i=0..100)]); # Robert Israel, Jan 13 2016
MATHEMATICA
Join[{0, 0}, Table[{k, k}, {n, 1, 6}, {k, 1, 2^n-1, 2}] // Flatten] // Accumulate (* Jean-François Alcover, Sep 19 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jan 02 2016
STATUS
approved