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 A047578 Numbers that are congruent to {2, 5, 6, 7} mod 8. 4
 2, 5, 6, 7, 10, 13, 14, 15, 18, 21, 22, 23, 26, 29, 30, 31, 34, 37, 38, 39, 42, 45, 46, 47, 50, 53, 54, 55, 58, 61, 62, 63, 66, 69, 70, 71, 74, 77, 78, 79, 82, 85, 86, 87, 90, 93, 94, 95, 98, 101, 102, 103, 106, 109, 110, 111, 114, 117, 118, 119, 122, 125 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..62. Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1). FORMULA G.f.: x*(1+x)*(x^2-x+2) / ((1+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011 a(n) = 2*n - cos(Pi*n/2). - Wesley Ivan Hurt, Oct 22 2013 From Wesley Ivan Hurt, May 20 2016: (Start) a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n > 4. a(n) = (4*n - i^(-n) - i^n)/2 where i=sqrt(-1). a(2n) = A047550(n), a(2n-1) = A016825(n-1). (End) Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2)*Pi/8 - log(2)/4. - Amiram Eldar, Dec 26 2021 MAPLE A047578:=n->2*n-cos(Pi*n/2): seq(A047578(n), n=1..100); # Wesley Ivan Hurt, Oct 22 2013 MATHEMATICA Flatten[#+{2, 5, 6, 7}&/@(8Range[0, 20])] (* Harvey P. Dale, Jan 26 2011 *) PROG (Sage) [lucas_number1(n, 0, 1)+2*n+2 for n in range(0, 56)] # Zerinvary Lajos, Jul 06 2008 CROSSREFS Cf. A016825, A047404, A047431, A047546, A047550, A056594. Sequence in context: A285032 A002157 A050002 * A259605 A367695 A284393 Adjacent sequences: A047575 A047576 A047577 * A047579 A047580 A047581 KEYWORD nonn,easy AUTHOR N. J. A. Sloane EXTENSIONS More terms from Wesley Ivan Hurt, May 20 2016 STATUS approved

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Last modified March 2 12:34 EST 2024. Contains 370467 sequences. (Running on oeis4.)