A068718 Boustrophedon transform of A068717 with A068717(1) = -1 instead of 0.

1, 2, 2, 2, 8, 25, 90, 404, 2055, 11792, 75053, 525622, 4015361, 33231679, 296182315, 2828335731, 28809181418, 311788442591, 3572832236720, 43216177809190, 550245463265240, 7356239983352887, 103028812072639378

Offset

0,2

Comments

Signs omitted, all terms < 0. A068717(1) = -1 means soluble (1*1 -1*0*0 = +1 resp. 0*0 -1*1*1 = -1).

Links

Table of n, a(n) for n=0..22.

Prog

(Python)
from itertools import accumulate, count, islice
from math import isqrt
from sympy import continued_fraction_periodic
def A068718_gen(): # generator of terms
    yield 1
    blist = (1, )
    for n in count(2):
        yield (blist := tuple(accumulate(reversed(blist), initial=0 if (a:=isqrt(n)**2==n) else (1 if len(continued_fraction_periodic(0, 1, n)[1]) & 1 else int(a)-1))))[-1]
A068718_list = list(islice(A068718_gen(), 40)) # Chai Wah Wu, Jun 14 2022

Crossrefs

Cf. A068716, A068717, A049240, A046951.

Sequence in context: A220177 A220805 A298647 * A075097 A138056 A340080

Adjacent sequences: A068715 A068716 A068717 * A068719 A068720 A068721

Keyword

nonn,easy

Author

Frank Ellermann, Feb 26 2002

Status

approved