OFFSET
0,2
COMMENTS
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.
LINKS
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).
FORMULA
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.
MATHEMATICA
A363773list[nmax_]:=LinearRecurrence[{4, 1, -4}, {1, 2, 7}, nmax+1]; A363773list[50] (* Paolo Xausa, Jun 29 2023 *)
PROG
(Python)
def A363773(n): return (1<<(n<<1|1))//5+1 # Chai Wah Wu, Jun 28 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Evangelos G. Filothodoros, Jun 21 2023
STATUS
approved