OFFSET
0,3
COMMENTS
The height of a term in A005132 = number of addition steps - number of subtraction steps to produce it.
Partial sums of A160357. - Allan C. Wechsler, Sep 08 2019
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..100000
Nick Hobson, Python program for this sequence
N. J. A. Sloane, FORTRAN program for A005132, A057167, A064227, A064228
EXAMPLE
A005132 begins 1, 3, 6, 2, 7, 13, 20, 12, ... and these terms have heights 1, 2, 3, 2, 3, 4, 5, 4, ...
MAPLE
g:= proc(n) is(n=0) end:
b:= proc(n) option remember; local t;
if n=0 then 0 else t:= b(n-1)-n; if t<=0 or g(t)
then t:= b(n-1)+n fi; g(t):= true; t fi
end:
a:= proc(n) option remember; `if`(n=0, 0,
a(n-1)+signum(b(n)-b(n-1)))
end:
seq(a(n), n=0..120); # Alois P. Heinz, Sep 08 2019
MATHEMATICA
g[n_] := n == 0;
b[n_] := b[n] = Module[{t}, If[n == 0, 0, t = b[n - 1] - n; If[t <= 0 || g[t], t = b[n - 1] + n]; g[t] = True; t]];
a[n_] := a[n] = If[n == 0, 0, a[n - 1] + Sign[b[n] - b[n - 1]]];
a /@ Range[0, 100] (* Jean-François Alcover, Apr 11 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Sep 25 2001
EXTENSIONS
a(0)=0 prepended by Allan C. Wechsler, Sep 08 2019
STATUS
approved