cp's OEIS Frontend

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

%I A363503 #64 Aug 02 2023 07:10:30
%S A363503 1,3,7,15,33,71,151,319,667,1385,2855,5855,11949,24299,49255,99597,
%T A363503 200967,404845,814425,1636581,3285713,6591853,13216829,26487447,
%U A363503 53062045,106265431,212759755,425890401,852381243,1705734905,3413043757,6828635653,13661395165
%N A363503 a(n+1) = 2*a(n) + A298338(n-1), with a(1) = 1.
%C A363503 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.
%H A363503 Evangelos G. Filothodoros, <a href="https://doi.org/10.48550/arXiv.2306.14652">Strongly coupled fermions in odd dimensions and the running cut-off Lambda_d</a>, arXiv:2306.14652 [hep-th], 2023.
%e A363503 a(1) = 1;
%e A363503 a(2) = 2*a(1) + 1 = 2*1 + 1 = 3;
%e A363503 etc.
%o A363503 (PARI) b(n) = if (n<=2, 1, b(n-1) + b(n-2) + b(n\2)); \\ A298338
%o A363503 a(n) = if (n==1, 1, 2*a(n-1) + b(n-2)); \\ _Michel Marcus_, Jun 06 2023
%o A363503 (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
%Y A363503 Cf. A104457 (phi^2), A298338.
%K A363503 nonn
%O A363503 1,2
%A A363503 _Evangelos G. Filothodoros_, Jun 06 2023