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A178243
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a(2n) = a(n), a(2n+1) = 10*a(n) + a(n+1).
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10
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1, 1, 11, 1, 21, 11, 111, 1, 31, 21, 221, 11, 221, 111, 1111, 1, 41, 31, 331, 21, 431, 221, 2221, 11, 331, 221, 2321, 111, 2221, 1111, 11111, 1, 51, 41, 441, 31, 641, 331, 3331, 21, 641, 431, 4531, 221, 4431, 2221, 22221, 11, 441, 331, 3531, 221, 4531, 2321, 23321
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OFFSET
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1,3
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COMMENTS
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Parsed into blocks of 1, 2, 4, 8,...term sums = powers of 12: (1, 12, 144,...).
A178569 is generated from a(2n) = 10*a(n); a(2n+1) = a(n) + a(n+1).
Polcoeff (1 + 10x + 11x^2 + ...) satisfies f(x)/f(x^2) = (1 + x + 10x^2).
Let q(x) = (1 + x + 10*x^2). Then (1 + 10x + 11x^2 + 100x^3 + ...) = q(x) * q(x^2) * q(x^4) * q(x^8) * ...
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LINKS
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FORMULA
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a(2n) = a(n), a(2n+1) = 10*a(n) + a(n+1) = row 10 in the array of A178239.
Let M = an infinite lower triangular matrix with (1, 1, 10, 0, 0, 0,...) in each column, shifted down twice from the previous column. This sequence is Lim_{n->inf} M^n, the left-shifted vector considered as a sequence.
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EXAMPLE
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a(6) = a(3) = 10 since a(2n) = a(n);
a(7) = 111 = 10*a(n) + a(n+1) = 10*11 + 1.
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MATHEMATICA
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a[1] = 1; a[n_] := a[n] = If[EvenQ@ n, a[n/2], 10 a[(n - 1)/2] + a[(n - 1)/2 + 1]]; Array[a, 55] (* Michael De Vlieger, May 20 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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