A128500 Numerators of partial sums for a series for Pi/(3*sqrt(3)).

1, 1, 1, 3, 11, 11, 97, 159, 159, 187, 1777, 1777, 26181, 23321, 23321, 51647, 797919, 797919, 16521821, 15228529, 15228529, 16404249, 351431887, 351431887, 1876142299, 1761735699, 1761735699, 1867970399, 51196569971, 51196569971

Offset: 0

Author

Wolfdieter Lang Apr 04 2007

Keywords

• nonn
• frac
• easy

Comments

The denominators are given in A128501.

The limit n -> infinity of the rationals r(n) defined below is Pi/(3*sqrt(3)).

Examples

			Rationals: [1, 1/2, 1/2, 3/4, 11/20, 11/20, 97/140, 159/280, 159/280, 187/280,...]
Pi/(3*sqrt(3))=+1/1 -1/2 +1/4 -1/5 +1/7 -1/8 +1/10 -1/11 +1/13 -+
		

Links

• W. Lang, Rationals and limit.

Formula

a(n)=numerator(r(n)) with the rationals r(n):=Sum_{k=0..n} ((-1)^k)*S(k,1)/(k+1) with Chebyshev's S-Polynomials S(k,1)=[1,1,0,-1,-1,0] periodic sequence with period 6. See A010892.