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A318722 Let f(0) = 0 and f(t*4^k + u) = i^t * ((1+i) * 2^k - f(u)) for any t in {1, 2, 3} and k >= 0 and u such that 0 <= u < 4^k (i denoting the imaginary unit); for any n >= 0, let g(n) = (f(A042968(n)) - 1 - i) / 2; a(n) is the real part of g(n). 3
-1, -1, 0, -1, -2, -2, -2, -2, -1, 0, 1, 1, -2, -3, -3, -1, -1, -2, -3, -4, -4, -4, -4, -3, -3, -3, -2, -3, -4, -4, -4, -4, -3, -2, -1, -1, 1, 2, 2, 0, 0, 1, 2, 3, 3, 3, 3, 2, -4, -5, -5, -3, -3, -4, -5, -6, -6, -6, -6, -5, -2, -2, -3, -2, -1, -1, -1, -1, -2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

See A318723 for the imaginary part of g.

See A318724 for the square of the modulus of g.

This sequence can be computed by considering the base 4 representation of A042968, hence the keyword base.

The function g runs uniquely through the set of Gaussian integers z such that Re(z) < 0 or Im(z) < 0.

The function g is related to the numbering of the cells in a Chair tiling (see representation of g(n) in Links section).

This sequence has similarities with A316657.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..12287

Rémy Sigrist, Colored scatterplot of (a(n), A318723(n)) for n = 0..3*4^9-1 (where the hue is function of n)

Rémy Sigrist, Colored scatterplot of (a(n), A318723(n)) for n = 0..3*4^9-1 (where the color is function of the sum of digits of A042968(n) in base 4)

Rémy Sigrist, Representation of g(n) for n = 0..3*4^2-1 in the complex plane, alongside the base 4 representation of A042968(n)

Tilings Encyclopedia, Chair

FORMULA

a(n) = A318723(n) iff the base 4 representation of A042968(n) contains only 0's and 2's.

If A048647(A042968(m)) = A042968(n), then a(m) = A318723(n) and A318723(m) = a(n).

PROG

(PARI) a(n) = my (d=Vecrev(digits(1+n+n\3, 4)), z=0); for (k=1, #d, if (d[k], z = I^d[k] * (-z + (1+I) * 2^(k-1)))); real((z-1-I)/2)

CROSSREFS

Cf. A042968, A048647, A318723, A318724.

Sequence in context: A334222 A124752 A293730 * A174344 A049241 A321858

Adjacent sequences:  A318719 A318720 A318721 * A318723 A318724 A318725

KEYWORD

sign,base

AUTHOR

Rémy Sigrist, Sep 02 2018

STATUS

approved

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Last modified June 5 11:52 EDT 2020. Contains 334840 sequences. (Running on oeis4.)