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A189672
Partial sums of A080846.
6
0, 1, 1, 1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 7, 7, 8, 9, 9, 10, 10, 10, 11, 12, 12, 13, 13, 13, 14, 14, 14, 15, 16, 16, 17, 17, 17, 18, 18, 18, 19, 20, 20, 21, 22, 22, 23, 23, 23, 24, 25, 25, 26, 27, 27, 28, 28, 28, 29, 30, 30, 31, 31, 31, 32, 32, 32, 33, 34, 34, 35, 36, 36, 37, 37, 37, 38, 39, 39, 40
OFFSET
1,5
COMMENTS
Almost identical to A189641.
LINKS
Kevin Ryde, Iterations of the Terdragon Curve, see index "TurnsR", with a(n) = TurnsR(n).
FORMULA
a(n) = floor((n+1)/3) + a(floor(n/3)), where a(0)=0.
MATHEMATICA
t = Nest[Flatten[# /. {0->{0, 1, 0}, 1->{0, 1, 1}}] &, {0}, 5] (*A080846*)
f[n_] := t[[n]]
Flatten[Position[t, 0]] (* A026225 conjectured *)
Flatten[Position[t, 1]] (* A026179 conjectured *)
s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;
Table[s[n], {n, 1, 120}] (*A189672*)
PROG
(PARI) a(n) = (n - vecsum(digits(n, 3)%2))/2; \\ Kevin Ryde, Apr 23 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Apr 25 2011
STATUS
approved