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A178569 a(2*n) = 10*a(n), a(2*n+1) = a(n) + a(n+1). 7
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 (list; graph; refs; listen; history; text; internal format)
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

Cf. A178568.

Sequence in context: A136830 A153069 A332703 * A332795 A303605 A266946

Adjacent sequences:  A178566 A178567 A178568 * A178570 A178571 A178572

KEYWORD

nonn

AUTHOR

Gary W. Adamson, May 29 2010

STATUS

approved

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Last modified May 6 11:12 EDT 2021. Contains 343581 sequences. (Running on oeis4.)