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Michel-Marie Deza, Mathieu Dutour Sikiric, and Mikhail Ivanovitch Shtogrin, <a href="https://doi.org/10.1007/978-81-322-2449-5">Geometric Structure of Chemistry-Relevant Graphs</a>, Springer, 2015; see Table 5.4 and Section 5.4.
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return c # Chai Wah Wu, May 16 2022
(Python)
def A088534(n):
c = 0
for y in range(n+1):
if y**2 > n:
break
for x in range(y+1):
z = x*(x+y)+y**2
if z > n:
break
elif z == n:
c += 1
return c # Chai Wah Wu, May 16 2022
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Also, apparently the number of 6-regular plane graphs with n vertices that have only trigonal faces and loops ("({1,3},6)-spheres" from the paper by Michel Deza and Mathieu Dutour Sikiric). - Andrey Zabolotskiy, Dec 22 2021
Oscar Marmon, Michel-Marie Deza, Mathieu Dutour Sikiric, Mikhail Ivanovitch Shtogrin, <a href="httphttps://arxivdoi.org/abs/math10.1007/0508201978Hexagonal Lattice Points on CirclesGeometric Structure of Chemistry-Relevant Graphs</a>, arXiv:math/0508201 [mathSpringer, 2015; see Table 5.4 and Section 5.NT], 20054.
Oscar Marmon, <a href="https://arxiv.org/abs/math/0508201">Hexagonal Lattice Points on Circles</a>, arXiv:math/0508201 [math.NT], 2005.
a(n) = ceiling(A004016(n)/12) = (A002324(n) + A145377(n)) / 2. - Andrey Zabolotskiy, Dec 23 2021