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A090678 a(n) = A088567(n) mod 2. 6
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified October 20 15:29 EDT 2019. Contains 328267 sequences. (Running on oeis4.)