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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)
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OFFSET
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0,2
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COMMENTS
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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
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REFERENCES
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Granino A. Korn and Theresa M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill Book Company, New York (1968).
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LINKS
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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.
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FORMULA
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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)
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MAPLE
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MATHEMATICA
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PROG
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(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
(GAP) Concatenation([0], List([1..60], n-> 4*n-2 )); # G. C. Greubel, Dec 30 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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