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A130824 a(n) = 2*A004273(n). 3
0, 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 114, 118, 122, 126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 182, 186, 190, 194, 198, 202, 206, 210, 214, 218, 222, 226, 230 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Equals A111284 from the 2nd term on. - R. J. Mathar, Jun 13 2008
Besides the first term, this sequence gives the denominators of the alternating series Pi/8 = 1/2 - 1/6 + 1/10 - 1/14 + 1/18 - 1/22 + .... - Mohammad K. Azarian, Oct 14 2011 [edited by Jon E. Schoenfield, Mar 07 2015]
Numbers that cannot be a side of a primitive Pythagorean triangle. - Torlach Rush, Nov 07 2019
Simple continued fraction expansion of tanh(1/2) = (e - 1)/(e + 1) = 1/(2 + 1/(6 + 1/(10 + 1/(14 + ...)))). - Peter Bala, Oct 01 2023
REFERENCES
Granino A. Korn and Theresa M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill Book Company, New York (1968).
LINKS
Mohammad K. Azarian, Problem 1218, Pi Mu Epsilon Journal, Vol. 13, No. 2, Spring 2010, p. 116. Solution published in Vol. 13, No. 3, Fall 2010, pp. 183-185.
FORMULA
From Stefano Spezia, Dec 09 2019: (Start)
G.f.: 2*x*(1+x)/(1-x)^2.
a(n) = 2*a(n-1) - a(n-2) for n > 0.
a(n) = 4*n - 1 - (-1)^(2^n). (End)
E.g.f: 2*(1 - (1-2*x)*exp(x)). - G. C. Greubel, Dec 30 2019
MAPLE
A130827 := proc(n) if n =0 then 0 ; else 4*n-2 ; fi ; end: seq(A130827(n), n=0..120) ; # R. J. Mathar, Oct 28 2007
MATHEMATICA
2 Join[{0}, Range[1, 200, 2]] (* Michael De Vlieger, Mar 07 2015 *)
PROG
(Magma) [4*n-2*Floor((n+2) mod (n+1)):n in [0..60]]; // Vincenzo Librandi, Sep 22 2011
(PARI) vector(61, n, if(n==1, 0, 4*(n-1) -2) ) \\ G. C. Greubel, Dec 30 2019
(Sage) [0]+[4*n-2 for n in (1..60)] # G. C. Greubel, Dec 30 2019
(GAP) Concatenation([0], List([1..60], n-> 4*n-2 )); # G. C. Greubel, Dec 30 2019
CROSSREFS
Sequence in context: A068977 A251538 A111284 * A016825 A161718 A122905
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Jul 17 2007
EXTENSIONS
More terms from R. J. Mathar, Oct 28 2007
STATUS
approved

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Last modified February 21 10:38 EST 2024. Contains 370228 sequences. (Running on oeis4.)