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A185184
Steps of the Hare in each tied Hare and Tortoise race of length n.
1
1, 0, 2, 1, 1, 0, 0, 3, 0, 2, 1, 1, 0, 2, 1, 1, 1, 0, 0, 0, 4, 0, 0, 3, 1, 0, 2, 0, 2, 0, 2, 1, 1, 1, 0, 0, 3, 1, 0, 2, 1, 1, 1, 0, 2, 1, 1, 1, 1, 0, 0, 0, 0, 5, 0, 0, 0, 4, 1, 0, 0, 3, 0, 2, 0, 0, 3, 1, 1, 0, 2, 0, 0, 3, 0, 2, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 1, 1, 1, 1, 0, 0, 0, 4, 1, 0, 0, 3, 1, 1, 0, 2, 0, 2, 1, 0, 2, 1, 1, 1, 1, 0, 0, 3, 1, 1, 0, 2, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0
OFFSET
1,3
COMMENTS
When the Hare bothers to move it only ever just catches up to the Tortoise.
This is an intermediate sequence between A030302 and A066099: omit the 0's from this sequence and we obtain A066099; map nonzero terms in this sequence to 1 and we obtain A030302.
FORMULA
a(i) = A030302(i) + number of consecutive 0 terms immediately preceding A030302(i).
EXAMPLE
The table begins:
1;
0 2, 1 1;
0 0 3, 0 2 1, 1 0 2, 1 1 1;
0 0 0 4, 0 0 3 1, 0 2 0 2, 0 2 1 1, 1 0 0 3, 1 0 2 1, 1 1 0 2, 1 1 1 1;
0 0 0 0 5, 0 0 0 4 1, 0 0 3 0 2, 0 0 3 1 1, 0 2 0 0 3, 0 2 0 2 1, 0 2 1 0 2, 0 2 1 1 1, 1 0 0 0 4, 1 0 0 3 1, 1 0 2 0 2, 1 0 2 1 1, 1 1 0 0 3, 1 1 0 2 1, 1 1 1 0 2, 1 1 1 1 1;
Mapping between sequences:
A030302: 110111001011101111000100110101011110011011110111110000100011
A185184: 10211003021102111000400310202021110031021110211110000500041
A066099: 1 211 3 211 2111 4 31 2 2 2111 31 2111 21111 5 41
CROSSREFS
Sequence in context: A250622 A212551 A125753 * A292894 A147701 A228348
KEYWORD
nonn,easy,tabf
AUTHOR
Jason Kimberley, Feb 27 2012
STATUS
approved