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A335359
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a(n) is the Y-coordinate of the n-th point of the Koch curve; sequence A335358 gives X-coordinates.
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2
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0, 0, 1, 0, 0, 1, 2, 2, 3, 2, 2, 1, 0, 0, 1, 0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 6, 6, 7, 8, 8, 9, 8, 8, 7, 6, 6, 7, 6, 6, 5, 4, 4, 3, 2, 2, 1, 0, 0, 1, 0, 0, 1, 2, 2, 3, 2, 2, 1, 0, 0, 1, 0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 6, 6, 7, 8, 8, 9, 10, 10, 11, 12
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OFFSET
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0,7
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COMMENTS
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Coordinates are given on a hexagonal lattice with X-axis and Y-axis as follows:
Y
/
/
0 ---- X
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LINKS
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FORMULA
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EXAMPLE
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The Koch curve starts (on a hexagonal lattice) as follows:
. . . . . . + . . . . . .
/8\
. . . . +---+ +---+ . . . .
6\ 7 9 /10
. . . + . + . + . + . . .
/2\ /5 \ / \
. +---+ +---+ . . +---+ +---+ .
0 1 3 4 12 13 15 16
Hence, a(6) = a(7) = a(9) = a(10) = 2.
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PROG
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(PARI) { hex = [1, I, I-1, -1, -I, 1-I]; z=0; for (n=0, 84, print1 (imag(z)", "); q=digits(n, 4); d=sum(k=1, #q, if (q[k]==1, +1, q[k]==2, -1, 0)); z+=hex[1+d%#hex]) }
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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