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A026430
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a(n) is the sum of first n terms of A001285 (Thue-Morse sequence).
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30
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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
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OFFSET
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0,3
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LINKS
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(Haskell)
a026430 n = a026430_list !! n
(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)
(Python)
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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approved
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