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, 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

Author

Peter Kagey, Feb 18 2017

Keywords

• nonn

Examples

			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.
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A282442, A282443.