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A282443
a(n) is the largest step size that is taken on a staircase of n steps when following the following procedure: Take steps of length 1 up a staircase until you can't step any further, then take steps of length 2 down until you can't step any further, and so on.
4
1, 2, 2, 3, 5, 4, 4, 8, 8, 7, 9, 10, 10, 14, 14, 10, 11, 17, 18, 15, 19, 16, 14, 23, 24, 17, 19, 27, 18, 23, 25, 20, 20, 30, 30, 19, 27, 24, 20, 31, 39, 32, 30, 38, 38, 24, 24, 34, 34, 50, 46, 31, 39, 53, 54, 47, 49, 40, 38, 59, 58, 57, 62, 58, 48, 49, 57, 39
OFFSET
1,2
FORMULA
a(n) = A282442(n) - 1.
EXAMPLE
For n = 4:
step size 1: 0 -> 1 -> 2 -> 3 -> 4;
step size 2: 4 -> 2 -> 0;
step size 3: 0 -> 3.
Because the walker cannot take four steps down, the biggest step size is 3.
Therefore a(4) = 3.
CROSSREFS
Sequence in context: A076228 A317050 A243970 * A210554 A208912 A210212
KEYWORD
nonn
AUTHOR
Peter Kagey, Feb 15 2017
STATUS
approved