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A377226
Take the sequence of the signed denominators of Leibniz series for Pi/4 (cf. A157142) and permute the terms so that a negative term follows every two positive terms and the absolute difference between two consecutive terms of the same sign is 4.
1
1, 5, -3, 9, 13, -7, 17, 21, -11, 25, 29, -15, 33, 37, -19, 41, 45, -23, 49, 53, -27, 57, 61, -31, 65, 69, -35, 73, 77, -39, 81, 85, -43, 89, 93, -47, 97, 101, -51, 105, 109, -55, 113, 117, -59, 121, 125, -63, 129, 133, -67, 137, 141, -71, 145, 149, -75, 153, 157, -79, 161
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.
FORMULA
a(n) = 2*a(n-3) - a(n-6) for n > 5.
a(n)= (9 + 12*n - 6*n*A061347(n) + 6*(2 + 3*n)*A049347(n+2))/9.
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]
KEYWORD
sign,easy
AUTHOR
Stefano Spezia, Oct 20 2024
STATUS
approved