A367554 a(n) is the number of 2n-regular circulant graphs of order 53.

1, 1, 13, 100, 578, 2530, 8866, 25300, 60115, 120175, 204347, 297160, 371516, 400024, 371516, 297160, 204347, 120175, 60115, 25300, 8866, 2530, 578, 100, 13, 1, 1

Offset: 0

Author

Andrey Zabolotskiy, Nov 22 2023

Keywords

• nonn
• fini
• full

Links

• Brian Alspach and Marni Mishna, Enumeration of Cayley graphs and digraphs, Discr. Math., 256 (2002), 527-539.
• Marni Mishna, Home page.
• Marni Mishna, Publications.
• Marni Mishna, Cayley Graph Enumeration, Master's Thesis, Simon Fraser University, 2000. See p. 16 (which is p. 24 in the pdf).

Crossrefs

Cf. A000031, A049287, A285620.

Programs

Python

from math import gcd, comb
from sympy import totient, divisors
def A367554(n): return sum(totient(d)*comb(26//d,n//d) for d in divisors(gcd(n,26),generator=True))//26 # Chai Wah Wu, Nov 23 2023

SageMath

def a(k, p):
    return (2/(p-1)) * sum(euler_phi(d) * binomial((p-1)/(2*d), k/(2*d)) for d in divisors(gcd(k, p-1)/2)) # see Mishna; beware the missing prefactor (2/(p-1))
print([a(2*n, 53) for n in range(27)]) # Andrey Zabolotskiy, Nov 22 2023

Formula

Sum_n a(n) = 2581428 = A049287(53) = A285620(53) = A000031((53-1)/2). - Andrey Zabolotskiy, Nov 22 2023