A093112 - OEIS (original) (raw)

-1, 7, 47, 223, 959, 3967, 16127, 65023, 261119, 1046527, 4190207, 16769023, 67092479, 268402687, 1073676287, 4294836223, 17179607039, 68718952447, 274876858367, 1099509530623, 4398042316799, 17592177655807, 70368727400447, 281474943156223, 1125899839733759

COMMENTS

Cletus Emmanuel calls these "Carol numbers".

FORMULA

a(n) = (2^n-1)^2 - 2.

a(n) = 6*a(n-1) - 7*a(n-2) - 6*a(n-3) + 8*a(n-4).

G.f.: x*(16*x^2-14*x+1) / ((x-1)*(2*x-1)*(4*x-1)). (End)

E.g.f.: 2 - exp(x) - 2*exp(2*x) + exp(4*x). - Stefano Spezia, Dec 09 2019

MATHEMATICA

Rest@ CoefficientList[Series[x (16 x^2 - 14 x + 1)/((x - 1) (2 x - 1) (4 x - 1)), {x, 0, 25}], x] (* Michael De Vlieger, Dec 09 2019 *)

LinearRecurrence[{7, -14, 8}, {-1, 7, 47}, 30] (* Harvey P. Dale, May 04 2026 *)

PROG

(PARI) Vec(x*(16*x^2-14*x+1)/((x-1)*(2*x-1)*(4*x-1)) + O(x^100)) \\ Colin Barker, Jul 07 2014

(Python)