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, 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.

Links

Table of n, a(n) for n=0..60.

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.

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]

Crossrefs

Cf. A003881, A005408, A049347, A061347, A131561, A157142, A377227.

Sequence in context: A075693 A198134 A082454 * A108245 A228789 A221715

Adjacent sequences: A377223 A377224 A377225 * A377227 A377228 A377229

Keyword

sign,easy

Author

Stefano Spezia, Oct 20 2024

Status

approved