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A282573
The number of steps taken on a staircase of n steps during the following routine: 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.
1
1, 3, 4, 7, 10, 12, 13, 19, 20, 23, 26, 32, 33, 39, 40, 41, 46, 53, 57, 56, 63, 65, 66, 77, 81, 80, 83, 94, 90, 97, 100, 102, 103, 117, 118, 117, 128, 126, 127, 138, 149, 151, 152, 162, 163, 160, 161, 175, 176, 194, 195, 186, 197, 212, 216, 215, 218, 220, 221
OFFSET
1,2
EXAMPLE
For n = 4:
step size 1: 0 -> 1 -> 2 -> 3 -> 4 (four steps);
step size 2: 4 -> 2 -> 0 (two steps);
step size 3: 0 -> 3 (one step).
Because the walker cannot take four steps down, a(4) = 4 + 2 + 1 = 7.
CROSSREFS
Sequence in context: A221975 A340603 A137294 * A177959 A371634 A360254
KEYWORD
nonn
AUTHOR
Peter Kagey, Feb 18 2017
STATUS
approved