A090678 a(n) = A088567(n) mod 2.

1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0

Offset

0,1

Comments

a(n) = -(-1)^[n/2]*A110036(n)/2 for n>=2, where A110036 gives the partial quotients of the continued fraction expansion of 1 + Sum_{n>=0} 1/x^(2^n). - Paul D. Hanna, Jul 09 2005

Links

Table of n, a(n) for n=0..104.

O. J. Rodseth and J. A. Sellers, On a Restricted m-Non-Squashing Partition Function, Journal of Integer Sequences, Vol. 8 (2005), Article 05.5.4.

N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, arXiv:math/0312418 [math.CO], 2003.

N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, Discrete Math., 294 (2005), 259-274.

Formula

b(0) == 1; if n is odd, b(n) == b(n-1) + 1; b(8m+2) == 1; b(8m+6) == 0; b(16m+4) == 0; b(16m+12) == 1; for m>0, b(16m) == b(8m), b(32m+8) == 0, b(32m+24) == 1. In other words, for m>0, b(8m) is the value of the bit immediately to the left of the rightmost 1 when m is written in binary.

a(n) = (-1)^floor(n/2)*A110037(n). - Paul D. Hanna, Jul 09 2005

Mathematica

nmax = 104; f = 1 + x/(1 - x) + Sum[x^(3*2^(k - 1))/Product[1 - x^(2^j), {j, 0, k}], {k, 1, Log[2, nmax]}];
a[n_] := Mod[SeriesCoefficient[f, {x, 0, n}], 2];
Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Jul 26 2018 *)

Prog

(PARI) {a(n)=(-1)^(n\2)*polcoeff(1+x-x^2*(1+x)/(1+x^2)+ sum(k=1, #binary(n), x^(3*2^(k-1))/prod(j=0, k, 1+x^(2^j)+x*O(x^n))), n)} /* Paul D. Hanna */

Crossrefs

b(8m) is (apart from the first term) A038189(m).

Cf. A110036, A110037.

Sequence in context: A115356 A115359 A117906 * A110037 A244528 A145379

Adjacent sequences: A090675 A090676 A090677 * A090679 A090680 A090681

Keyword

nonn

Author

N. J. A. Sloane, Dec 20 2003

Status

approved