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 A047220 Numbers that are congruent to {0, 1, 3} mod 5. 24
 0, 1, 3, 5, 6, 8, 10, 11, 13, 15, 16, 18, 20, 21, 23, 25, 26, 28, 30, 31, 33, 35, 36, 38, 40, 41, 43, 45, 46, 48, 50, 51, 53, 55, 56, 58, 60, 61, 63, 65, 66, 68, 70, 71, 73, 75, 76, 78, 80, 81, 83, 85, 86, 88, 90, 91, 93, 95, 96, 98, 100, 101, 103, 105, 106 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS First differences are (1,2,2), repeat, with period 3 (A130196). - N. J. A. Sloane, Dec 03 2015 Also numbers k such that k*(k+2)*(k+4) is divisible by 5. - Bruno Berselli, Dec 28 2017 Maximum sum of degeneracies over all decompositions of the complete graph of order n into four factors. The extremal decompositions are characterized in the Bickle link below. - Allan Bickle, Dec 21 2021 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Allan Bickle, Nordhaus-Gaddum Theorems for k-Decompositions, Congr. Num. 211 (2012) 171-183. Z. Furedi, A. Kostochka, M. Stiebitz, R. Skrekovski, and D. West, Nordhaus-Gaddum-type theorems for decompositions into many parts, J. Graph Theory 50 (2005), 273-292. Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1). FORMULA a(n) = floor(5*(n-1)/3). - Gary Detlefs, Feb 20 2010 a(n) = 2*n - floor(n/3) - (n^2 mod 3), with offset 0. - Gary Detlefs, Mar 19 2010 G.f.: x^2*(1 + 2*x + 2*x^2)/(1 - x)^2/(1 + x + x^2). - Colin Barker, Feb 17 2012 a(n) = n + floor(2*(n-1)/3) - 1. - Arkadiusz Wesolowski, Sep 18 2012 From Wesley Ivan Hurt, Jun 14 2016: (Start) a(n) = a(n-1) + a(n-3) - a(n-4) for n>4. a(n) = 5*n/3 - 2 + 2*sin(2*n*Pi/3)/(3*sqrt(3)). a(3*k) = 5*k-2, a(3*k-1) = 5*k-4, a(3*k-2) = 5*k-5. (End) E.g.f.: 2 + (5*x - 6)*exp(x)/3 + 2*sin(sqrt(3)*x/2)*(cosh(x/2) - sinh(x/2))/(3*sqrt(3)). - Ilya Gutkovskiy, Jun 14 2016 MAPLE seq(floor(5*(n-1)/3), n=1..56); # Gary Detlefs, Feb 20 2010 seq(2*n-floor(n/3)-(n^2 mod 3), n=0..55); # Gary Detlefs, Mar 19 2010 MATHEMATICA Table[Floor[5*(n-1)/3], {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Jan 28 2012 *) PROG (Magma) I:=[0, 1, 3, 5]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // Vincenzo Librandi, Apr 26 2012 (PARI) a(n)=n + 2*(n-1)\3 - 1 \\ Charles R Greathouse IV, Sep 24 2015 CROSSREFS Cf. A011655, A130196 (first differences). Sequence in context: A247913 A188046 A244644 * A329845 A329993 A064994 Adjacent sequences: A047217 A047218 A047219 * A047221 A047222 A047223 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified March 23 18:29 EDT 2023. Contains 361449 sequences. (Running on oeis4.)