A026430 a(n) is the sum of first n terms of A001285 (Thue-Morse sequence).

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

Offset

0,3

Links

Winston de Greef, Table of n, a(n) for n = 0..10000 (first 1001 terms from T. D. Noe)

Nicholas John Bizzell-Browning, LIE scales: Composing with scales of linear intervallic expansion, Ph. D. Thesis, Brunel Univ. (UK, 2024). See p. 143.

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

Adjacent sequences: A026427 A026428 A026429 * A026431 A026432 A026433

Keyword

nonn,nice

Author

Clark Kimberling

Status

approved