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

%I #13 Nov 23 2023 15:15:48

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

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

%U 1,1

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

%H Brian Alspach and Marni Mishna, <a href="https://doi.org/10.1016/S0012-365X(02)00319-9">Enumeration of Cayley graphs and digraphs</a>, Discr. Math., 256 (2002), 527-539.

%H Marni Mishna, <a href="https://www.sfu.ca/~mmishna/">Home page</a>.

%H Marni Mishna, <a href="https://www.sfu.ca/~mmishna/research.html">Publications</a>.

%H Marni Mishna, <a href="https://www.sfu.ca/~mmishna/PUB/sfu-thesis.pdf">Cayley Graph Enumeration</a>, Master's Thesis, Simon Fraser University, 2000. See p. 16 (which is p. 24 in the pdf).

%F Sum_n a(n) = 2581428 = A049287(53) = A285620(53) = A000031((53-1)/2). - _Andrey Zabolotskiy_, Nov 22 2023

%o (SageMath)

%o def a(k, p):

%o 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))

%o print([a(2*n, 53) for n in range(27)]) # _Andrey Zabolotskiy_, Nov 22 2023

%o (Python)

%o from math import gcd, comb

%o from sympy import totient, divisors

%o 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

%Y Cf. A000031, A049287, A285620.

%K nonn,fini,full

%O 0,3

%A _Andrey Zabolotskiy_, Nov 22 2023