A246017 Partial sums of A246016.

1, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 6, 5, 4, 5, 4, 5, 6, 5, 6, 7, 6, 7, 8, 7, 8, 7, 6, 7, 8, 7, 8, 7, 6, 7, 6, 5, 6, 5, 4, 5, 6, 5, 6, 7, 6, 7, 8, 7, 8, 7, 6, 7, 8, 7, 8, 9, 8, 9, 10, 9, 8, 9, 8, 9, 10, 9, 10, 11, 10, 11, 12, 11, 10, 11, 10, 9, 10, 9, 8, 9, 8, 9, 10, 9, 8, 9, 8

Offset

0,2

Comments

This sequence and A246016 are the subject of the Lafrance et al. (2014) paper.

Links

Altug Alkan, Table of n, a(n) for n = 0..10000

Philip Lafrance, Narad Rampersad, Randy Yee, Some properties of a Rudin-Shapiro-like sequence, arXiv:1408.2277 [math.CO], 2014.

Mathematica

b[n_] := b[n] = If[n == 0, 0, If[EvenQ[n], b[n/2] + DigitCount[n/2, 2, 1], b[(n - 1)/2] + 1]];
a55941[n_] := b[n] - DigitCount[n, 2, 1];
a[n_] := Sum[(-1)^a55941[k], {k, 0, n}];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Sep 23 2018 *)

Prog

(PARI) a055941(n) = {my(b=binary(n)); nb = 0; for (i=1, #b-1, if (b[i], nb += sum(j=i+1, #b, !b[j])); ); nb; }
a(n) = sum(k=0, n, (-1)^a055941(k));
(Python)
def A246017(n):
    c = 0
    for k in range(n+1):
        a, b = 0, 1
        for i, j in enumerate(bin(k)[:1:-1]):
            if int(j):
                a ^= (i&1)^(b:=b^1)
        c += -1 if a else 1
    return c # Chai Wah Wu, Jul 26 2023

Crossrefs

Cf. A055941, A161511, A246016.

Sequence in context: A033923 A233420 A220098 * A116939 A253174 A008611

Adjacent sequences: A246014 A246015 A246016 * A246018 A246019 A246020

Keyword

nonn,look

Author

Michel Marcus and N. J. A. Sloane, Aug 13 2014

Status

approved