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

0,3

Links

Table of n, a(n) for n=0..26.

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).

Formula

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

Prog

(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
(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

Crossrefs

Cf. A000031, A049287, A285620.

Sequence in context: A089936 A196928 A266002 * A326864 A083341 A336347

Adjacent sequences: A367551 A367552 A367553 * A367555 A367556 A367557

Keyword

nonn,fini,full

Author

Andrey Zabolotskiy, Nov 22 2023

Status

approved