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A110037 Signed version of A090678 and congruent to A088567 mod 2. 1
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]*A090678(n) = A088567(n) mod 2, where A088567(n) equals the number of "non-squashing" partitions of n. a(n) = -A110036(n)/2 for n>=2, where the A110036 gives the partial quotients of the continued fraction expansion of 1 + Sum_{n>=0} 1/x^(2^n).

LINKS

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

FORMULA

G.f.: A(x) = 1+x - x^2*(1+x)/(1+x^2) + Sum_{k>=1} x^(3*2^(k-1))/Product_{j=0..k} (1+x^(2^j)).

PROG

(PARI) {a(n)=polcoeff(A=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)}

CROSSREFS

Cf. A110036, A090678, A088567.

Sequence in context: A115359 A117906 A090678 * A244528 A145379 A258869

Adjacent sequences:  A110034 A110035 A110036 * A110038 A110039 A110040

KEYWORD

sign

AUTHOR

Paul D. Hanna, Jul 09 2005

STATUS

approved

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Last modified March 23 09:20 EDT 2019. Contains 321424 sequences. (Running on oeis4.)