A323259 a(n) is the Y-coordinate of the n-th point of the first type of Wunderlich curve (starting at the origin and occupying the first quadrant).

0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 4, 5, 5, 4, 3, 3, 4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 7, 6, 6, 7, 8, 8, 7, 6, 5, 5, 5, 4, 4, 4, 3, 3, 3, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 4, 5, 5, 4, 3, 3, 4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 10, 11, 11, 10

Offset: 1

Author

Rémy Sigrist, Jan 09 2019

Keywords

• nonn

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..6561
• Index entries for sequences related to coordinates of 2D curves

Crossrefs

See A323258 for the X-coordinate and additional comments.

Programs

PARI

s = [0, 1, 2, 2+I, 1+I, I, 2*I, 1+2*I, 2+2*I];
w = apply(z -> imag(z) + I*real(z), s);
r = [0, 1, 0, 3, 2, 3, 0, 1, 0]
a(n) = {
    my (d=if (n>1, Vecrev(digits(n-1, 9)), [0]), z=s[1+d[1]]);
    for (i=2, #d,
        my (c=(3^(i-1)-1)/2*(1+I));
        z = 3^(i-1) * w[1+d[i]] + c + (z-c) * I^r[1+d[i]];
    );
    return (imag(z));
}