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

Author

Clark Kimberling

Keywords

• nonn
• nice

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.

Crossrefs

Cf. A001285, A356133 (complement).

Cf. A115384.

Programs

Haskell

a026430 n = a026430_list !! n
a026430_list = scanl (+) 0 a001285_list -- Reinhard Zumkeller, Jun 28 2013

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 *)

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

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