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proposed
approved
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Revision History for A005590
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
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editing
proposed
LINKS
B. Bruce Reznick, <a href="http://projecteuclid.org/euclid.ijm/1256045729">Some extremal problems for continued fractions</a>, Ill. J. Math., 29 (1985), 261-279.
R. Ralf Stephan, <a href="httphttps://arXivarxiv.org/abs/math.CO/0307027">Divide-and-conquer generating functions. I. Elementary sequences</a>, arXiv:math/0307027 [math.CO], 2003.
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proposed
editing
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editing
proposed
COMMENTS
Let M = a triangular matrix with (1, 1, -1, 0, 0, 0, ...) in every column >k=1 shifted down twice from the previous column. Then A005590 starting with 1 = Lim_lim_{n->infinfinity} M^n, the left-shifted vector considered as a sequence. - Gary W. Adamson, Apr 13 2010
FORMULA
a(2^k*n+1) = a(n+1) - k*a(n);
a(2^k*n+3) = a(n) for k >= 2;
a(2^k*n+5) = -a(2^(k-1)*n+1) for k >= 3;
a(2^k*n+7) = a(2^(k-2)*n+1) for k >= 4;
a(2^k*n+2^k-1) = a(n) if k is even;
a(2^k*n+2^k-1) = a(n+1)-a(n)= a(2*n+1) if k is odd.
a(2^k+1) = 1-k;
a(2^k+3) = 1 for k >= 2;
a(2^k+5) = k-2 for k >= 3;
a(2^k+7) = 3-k for k >= 4;
a(2^k-1) = 0 if k is even;
a(2^k-1) = 1 if k is odd.
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approved
editing
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reviewed
approved
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proposed
reviewed
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editing
proposed
PROG
l.append(l[n//2] if n%2==0 else l[(n + 1)//2] - l[(n - 1)//2])
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approved
editing
STATUS
reviewed
approved