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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.

%I A282573 #8 Feb 19 2017 09:21:38
%S A282573 1,3,4,7,10,12,13,19,20,23,26,32,33,39,40,41,46,53,57,56,63,65,66,77,
%T A282573 81,80,83,94,90,97,100,102,103,117,118,117,128,126,127,138,149,151,
%U A282573 152,162,163,160,161,175,176,194,195,186,197,212,216,215,218,220,221
%N 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.
%H A282573 Peter Kagey, <a href="/A282573/b282573.txt">Table of n, a(n) for n = 1..10000</a>
%e A282573 For n = 4:
%e A282573 step size 1: 0 -> 1 -> 2 -> 3 -> 4 (four steps);
%e A282573 step size 2: 4 -> 2 -> 0 (two steps);
%e A282573 step size 3: 0 -> 3 (one step).
%e A282573 Because the walker cannot take four steps down, a(4) = 4 + 2 + 1 = 7.
%Y A282573 Cf. A282442, A282443.
%K A282573 nonn
%O A282573 1,2
%A A282573 _Peter Kagey_, Feb 18 2017