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A026430 a(n) is the sum of first n terms of A001285 (Thue-Morse sequence). 30
0, 1, 3, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 19, 21, 23, 24, 26, 27, 28, 30, 31, 33, 35, 36, 37, 39, 41, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 57, 59, 60, 61, 63, 65, 66, 68, 69, 70, 72, 73, 75, 77, 78, 80, 81, 82, 84, 86, 87, 88, 90, 91, 93 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Winston de Greef, Table of n, a(n) for n = 0..10000 (first 1001 terms from T. D. Noe)
FORMULA
a(0)=0, a(1)=1, a(2n) = 3n, a(2n+1) = -a(n) + a(n+1) + 3n. - Ralf Stephan, Oct 08 2003
G.f.: x*(3/(1 - x)^2 - Product_{k>=1} (1 - x^(2^k)))/2. - Ilya Gutkovskiy, Apr 03 2019
MATHEMATICA
A001285 = Table[ Mod[ Sum[ Mod[ Binomial[n, k], 2], {k, 0, n}], 3], {n, 0, 61}]; Accumulate[A001285] (* Jean-François Alcover, Sep 25 2012 *)
Join[{0}, Accumulate[1 + ThueMorse /@ Range[0, 100]]] (* Jean-François Alcover, Sep 18 2019, from version 10.2 *)
PROG
(Haskell)
a026430 n = a026430_list !! n
a026430_list = scanl (+) 0 a001285_list -- Reinhard Zumkeller, Jun 28 2013
(PARI) first(n)=my(v=vector(n)); v[1]=1; for(k=2, n, v[k]=if(k%2, v[k\2+1]-v[k\2])+k\2*3); concat(0, v) \\ Charles R Greathouse IV, May 09 2016
(Python)
from itertools import accumulate, islice
def A026430_gen(): # generator of terms
yield from (0, 1)
blist, s = [1], 1
while True:
c = [3-d for d in blist]
blist += c
yield from (s+d for d in accumulate(c))
s += sum(c)
A026430_list = list(islice(A026430_gen(), 30)) # Chai Wah Wu, Feb 22 2023
(Python)
def A026430(n): return n+(n-1>>1)+(n-1&1|(n.bit_count()&1^1)) # Chai Wah Wu, Mar 01 2023
CROSSREFS
Cf. A001285, A356133 (complement).
Cf. A115384.
Sequence in context: A242535 A165290 A307206 * A002150 A153264 A249595
KEYWORD
nonn,nice
AUTHOR
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)