OFFSET
0,2
REFERENCES
Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.4.1, p. 20.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).
FORMULA
a(n) = 2*a(n-3) - a(n-6) for n > 5.
G.f.: (1 + 5*x - 3*x^2 + 7*x^3 + 3*x^4 - x^5)/(1 - x^3)^2.
E.g.f.: exp(-x/2)*(3*exp(3*x/2)*(3 + 4*x) + 12*x*cos(sqrt(3)*x/2) + 4*sqrt(3)*(2 - 3*x)*sin(sqrt(3)*x/2))/9.
Sum_{n>=0} 1/a(n) = (log(2) + Pi)/4 = A377227.
MATHEMATICA
LinearRecurrence[{0, 0, 2, 0, 0, -1}, {1, 5, -3, 9, 13, -7}, 61]
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Stefano Spezia, Oct 20 2024
STATUS
approved