A213088 The Manhattan distance to the origin while traversing the first quadrant in a taxicab geometry.

0, 1, 2, 1, 2, 3, 4, 3, 2, 3, 4, 5, 6, 5, 4, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 6, 7, 8, 9, 10, 11, 12, 11, 10, 9, 8, 7, 6, 7, 8, 9, 10, 11, 12, 13, 14, 13, 12, 11, 10, 9, 8, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 15, 14, 13, 12, 11

Offset

1,3

Links

Table of n, a(n) for n=1..78.

Prog

(Python)
def f(x, y):
    if not x and y % 2:
        y = y + 1
    elif not y and not x % 2:
        x = x + 1
    elif x == y:
        if x % 2:
            x = x - 1
        else:
            y = y - 1
    elif y < x:
        if x % 2:
            y = y + 1
        else:
            y = y - 1
    else:
        if y % 2:
            x = x - 1
        else:
            x = x + 1
    return x, y
res = []
x = y = 0
for i in range(100):
    res.append(x + y)
    x, y = f(x, y)
print(res)

Crossrefs

Sequence in context: A030307 A175792 A196686 * A357564 A169809 A214962

Adjacent sequences: A213085 A213086 A213087 * A213089 A213090 A213091

Keyword

nonn,walk

Author

Jens Ahlström, Jun 05 2012

Status

approved