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

Author

Frank Ellermann, Feb 26 2002

Keywords

• nonn
• easy

Comments

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

Crossrefs

Cf. A068716, A068717, A049240, A046951.

Programs

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