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 A047273 Numbers that are congruent to {0, 1, 3, 5} mod 6. 11
 0, 1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19, 21, 23, 24, 25, 27, 29, 30, 31, 33, 35, 36, 37, 39, 41, 42, 43, 45, 47, 48, 49, 51, 53, 54, 55, 57, 59, 60, 61, 63, 65, 66, 67, 69, 71, 72, 73, 75, 77, 78, 79, 81, 83, 84, 85, 87, 89, 90, 91, 93, 95, 96, 97, 99, 101, 102, 103 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Complement of A047235; A093719(a(n)) = 1. - Reinhard Zumkeller, Oct 01 2008 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1). FORMULA G.f.: x*(1+x+x^2)/((1-x)^2*(1+x^2)) = x*(1-x^2)*(1-x^3)/((1-x)^3*(1-x^4)). a(n) = n + A004524(n+1) = -a(-n) for all n in Z. Starting (1, 3, 5, ...) = partial sums of (1, 2, 2, 1, 1, 2, 2, 1, 1, ...). - Gary W. Adamson, Jun 19 2008 a(n) = 2*(n-floor(n/4)) - (3-I^n-(-I)^n-(-1)^n)/4, with offset 0..a(0)=0. - Gary Detlefs, Mar 19 2010 a(n) = (3*n-3+cos(Pi*n/2))/2. - R. J. Mathar, Oct 08 2010 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) = (6*n-6+(-1)^(n/2)+(-1)^(-n/2))/4. (End) Euler transform of length 4 sequence [3, -1, -1, 1]. - Michael Somos, Jun 24 2017 MAPLE seq(2*(n-floor(n/4)) - (3-I^n-(-I)^n-(-1)^n)/4, n = 0..69); # Gary Detlefs, Mar 19 2010 MATHEMATICA LinearRecurrence[{2, -2, 2, -1}, {0, 1, 3, 5}, 80] (* Harvey P. Dale, Jan 04 2015 *) PROG (PARI) a(n)=n+(n+1)\4+(n+2)\4 (Sage) [(lucas_number1(n+2, 0, 1)+3*n)/2 for n in xrange(0, 70)] # Zerinvary Lajos, Mar 09 2009 (Haskell) a047273 n = a047273_list !! (n-1) a047273_list = 0 : 1 : 3 : 5 : map (+ 6) a047273_list -- Reinhard Zumkeller, Feb 19 2013 (MAGMA) [[(6*n-6+(-1)^(n div 2)+(-1)^(-n div 2))/4: n in [1..100]]; // Wesley Ivan Hurt, May 20 2016 CROSSREFS Cf. A004524, A007310, A047228, A047235, A047241, A047261, A093719, A096981. First differences of A281026. See A301729 for an essentially identical sequence. Sequence in context: A189669 A164028 A301729 * A232744 A284015 A286908 Adjacent sequences:  A047270 A047271 A047272 * A047274 A047275 A047276 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified October 18 02:23 EDT 2019. Contains 328135 sequences. (Running on oeis4.)