Evangelos G. Filothodoros - cp's OEIS frontend

User: Evangelos G. Filothodoros

Evangelos G. Filothodoros has authored 2 sequences.

A363503 a(n+1) = 2*a(n) + A298338(n-1), with a(1) = 1.

1, 3, 7, 15, 33, 71, 151, 319, 667, 1385, 2855, 5855, 11949, 24299, 49255, 99597, 200967, 404845, 814425, 1636581, 3285713, 6591853, 13216829, 26487447, 53062045, 106265431, 212759755, 425890401, 852381243, 1705734905, 3413043757, 6828635653, 13661395165

Offset: 1

Evangelos G. Filothodoros, Jun 06 2023

nonn

a(n) is an odd number that appears in m* = log(a(n)*phi^2) for the fermion condensate mass in odd dimensional and large N Gross-Neveu model at imaginary chemical potential and finite temperature.

			a(1) = 1;
a(2) = 2*a(1) + 1 = 2*1 + 1 = 3;
etc.

Evangelos G. Filothodoros, Strongly coupled fermions in odd dimensions and the running cut-off Lambda_d, arXiv:2306.14652 [hep-th], 2023.

Cf. A104457 (phi^2), A298338.

b(n) = if (n<=2, 1, b(n-1) + b(n-2) + b(n\2)); \\ A298338
a(n) = if (n==1, 1, 2*a(n-1) + b(n-2)); \\ Michel Marcus, Jun 06 2023

first(n) = {n = max(3, n); my(A298338 = vector(n+1), res = vector(n)); res[1] = 1; for(i = 1, 3, A298338[i] = 1); for(i = 4, n+1, A298338[i] = A298338[i-1] + A298338[i-2] + A298338[(i-1)\2 + 1]); for(i = 2, n, res[i] = 2*res[i-1] + A298338[i-1]); res} \\ David A. Corneth, Jun 08 2023

A363773 a(n) = (4^(n+1) + (-1)^n + 5)/10.

Original entry on oeis.org

1, 2, 7, 26, 103, 410, 1639, 6554, 26215, 104858, 419431, 1677722, 6710887, 26843546, 107374183, 429496730, 1717986919, 6871947674, 27487790695, 109951162778, 439804651111, 1759218604442, 7036874417767, 28147497671066, 112589990684263, 450359962737050

Offset: 0

Evangelos G. Filothodoros, Jun 21 2023

a(n) is a part of the numerator of the approximate solutions x(n) = (Pi/2)*(1+5/((4^(n+1)-(-1)^(n+1)))) = a(n)*Pi/A015521(n+1) of D_d(exp(-i*x(n))) = Cl_d(x(n)+Pi) = 0, where D_d(exp(-i*x(n))) is the Bloch-Wigner-Ramakrishnan polylogarithm function and Cl_d(x(n)+Pi) is the Clausen function for odd d >= 3 and n >= 0.

Paolo Xausa, Table of n, a(n) for n = 0..1000
Evangelos G. Filothodoros, Anastasios C. Petkou, and Nicholas D. Vlachos, The fermion-boson map for large d, Nuclear Physics B, Volume 941, 2019, pp. 195-224.
Index entries for linear recurrences with constant coefficients, signature (4,1,-4).

Cf. A015521, A037481.

A363773list[nmax_]:=LinearRecurrence[{4,1,-4},{1,2,7},nmax+1];A363773list[50] (* Paolo Xausa, Jun 29 2023 *)

def A363773(n): return (1<<(n<<1|1))//5+1 # Chai Wah Wu, Jun 28 2023

a(n) = 1 + A037481(n).
G.f.: (1-2*x-2*x^2)/((x-1)*(4*x-1)*(x+1)).
E.g.f.: (4*e^(4*x) + e^-x + 5*e^x)/10.

cp's OEIS Frontend

User: Evangelos G. Filothodoros

A363503 a(n+1) = 2*a(n) + A298338(n-1), with a(1) = 1.

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