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

Author

Evangelos G. Filothodoros, Jun 06 2023

Keywords

• nonn

Comments

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.

Examples

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

Links

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

Crossrefs

Cf. A104457 (phi^2), A298338.

Programs

PARI

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

PARI

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