

A178569


a(2*n) = 10*a(n), a(2*n+1) = a(n) + a(n+1).


2



1, 10, 11, 100, 21, 110, 111, 1000, 121, 210, 131, 1100, 221, 1110, 1111, 10000, 1121, 1210, 331, 2100, 341, 1310, 1231, 11000, 1321, 2210, 1331, 11100, 2221, 11110, 11111, 100000, 11121, 11210, 2331, 12100, 1541, 3310, 2431, 21000, 2441, 3410, 1651, 13100, 2541, 12310, 12231, 110000, 12321, 13210
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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 leftshifted 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^(n1);
elif type(n, 'even') then
10*procname(n/2);
else
procname((n1)/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[(n1)/2] + a[(n+1)/2], 10*a[n/2]]; Array[a, 50] (* G. C. Greubel, Jan 30 2019 *)


CROSSREFS

Cf. A178568.
Sequence in context: A045953 A136830 A153069 * A303605 A266946 A081551
Adjacent sequences: A178566 A178567 A178568 * A178570 A178571 A178572


KEYWORD

nonn


AUTHOR

Gary W. Adamson, May 29 2010


STATUS

approved



