OFFSET
1,2
COMMENTS
Equals row 10 in the array of A178568.
Polcoeff f(x)= (1 + 10x + 11x^2 + ...) satisfies f(x)/f(x^2) = (1 +10*x + x^2).
Let q(x) = (1 + 10*x + x^2). Then polcoeff f(x) = q(x) * q(x^2) * q(x^4) * q(x^8) * ...
The sequence mod 10 = (1, 0, 1, 0, 1, 0,...)
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
FORMULA
a(2*n) = 10*a(n), a(2*n+1) = a(n) + a(n+1). Let M = an infinite lower triangular matrix with (1, 10, 1, 0, 0, 0,...) in each column; with each column >1 shifted down twice from the previous column. Then A178570 = Lim_{n->inf} M^n, the left-shifted vector considered as a sequence.
EXAMPLE
a(6) = 110 = 10*a(5) = 10*11.
a(7) = 111 = a(3) + a(4) = 111 + 100.
MAPLE
A178569 := proc(n)
option remember;
if n <= 2 then
10^(n-1);
elif type(n, 'even') then
10*procname(n/2);
else
procname((n-1)/2)+procname((n+1)/2) ;
end if;
end proc: # R. J. Mathar, Jul 21 2015
MATHEMATICA
a[1]=1; a[2]=10; a[n_]:= a[n]= If[OddQ@n, a[(n-1)/2] + a[(n+1)/2], 10*a[n/2]]; Array[a, 50] (* G. C. Greubel, Jan 30 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Gary W. Adamson, May 29 2010
STATUS
approved