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A332384
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a(n) is the Y-coordinate of the n-th point of the dragon curve. Sequence A332383 gives X-coordinates.
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5
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0, 0, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 0, 0, -1, -1, 0, 0, -1, -1, -2, -2, -1, -1, -2, -2, -3, -3, -4, -4, -5, -5, -4, -4, -5, -5, -6, -6, -5, -5, -6, -6, -5, -5, -4, -4, -3, -3, -4, -4, -5, -5, -6, -6, -5, -5, -6, -6, -7, -7, -8, -8, -9, -9, -8, -8, -9, -9, -10
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OFFSET
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0,5
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LINKS
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FORMULA
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For any k >= 0:
- a(2^(4*k)) = 0,
- a(2^(4*k+1)) = (-4)^k,
- a(2^(4*k+2)) = 2*(-4)^k,
- a(2^(4*k+3)) = 2*(-4)^k.
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MATHEMATICA
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Im[Join[{0}, Accumulate[Nest[Join[#, Reverse[I #]] &, {1}, 7]]]] (* Vladimir Reshetnikov, Apr 14 2022 *)
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PROG
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(PARI) A014577(n)=1/2*(1+(-1)^(1/2*((n+1)/2^valuation(n+1, 2)-1)))
{ z=0; d=1; for (n=0, 68, print1 (imag(z) ", "); z += d; d*=if (A014577(n), +I, -I)) }
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CROSSREFS
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KEYWORD
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sign,base
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AUTHOR
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STATUS
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approved
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