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A162330
Blocks of 4 numbers of the form 2k, 2k-1, 2k, 2k+1, k=1,2,3,4,...
7
2, 1, 2, 3, 4, 3, 4, 5, 6, 5, 6, 7, 8, 7, 8, 9, 10, 9, 10, 11, 12, 11, 12, 13, 14, 13, 14, 15, 16, 15, 16, 17, 18, 17, 18, 19, 20, 19, 20, 21, 22, 21, 22, 23, 24, 23, 24, 25, 26, 25, 26, 27, 28, 27, 28, 29, 30, 29, 30, 31, 32, 31, 32, 33, 34, 33, 34, 35, 36, 35, 36, 37, 38, 37
OFFSET
1,1
COMMENTS
This illustrates the infinite product Pi/2 = Product_{k>=1} ((2*k)/(2k-1))*((2k)/(2k+1)): read the 4 terms of numerator and denominator of the factor in the product in that order shown.
Number of roots of the polynomial 1+x+x^2+...+x^(n+1) = (x^(n+2)-1)/(x-1) in the left half plane. - Michel Lagneau, Oct 30 2012
LINKS
FORMULA
a(n) = a(n-1) + a(n-4) - a(n-5).
G.f.: x*(2-x+x^2+x^3-x^4)/((1+x)*(1+x^2)*(1-x)^2).
a(n) = n + 1 - 2*floor( (n+2)/4 ). - M. F. Hasler, Nov 01 2012
a(n) = (2*n + 3 - (-1)^n + 2*(-1)^((2*n - 1 + (-1)^n)/4))/4. - Luce ETIENNE, Mar 08 2016
Sum_{n>=1} (-1)^n/a(n) = 2*log(2) - 1. - Amiram Eldar, Sep 10 2023
MATHEMATICA
Flatten[#+{0, -1, 0, 1}&/@Range[2, 40, 2]] (* Harvey P. Dale, Aug 12 2014 *)
PROG
(PARI) A162330(n)=n+1-(n+2)\4*2 \\ M. F. Hasler, Nov 01 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Edited by R. J. Mathar, Sep 16 2009
STATUS
approved