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 A047357 Numbers that are congruent to {0, 1, 3} mod 7. 1
 0, 1, 3, 7, 8, 10, 14, 15, 17, 21, 22, 24, 28, 29, 31, 35, 36, 38, 42, 43, 45, 49, 50, 52, 56, 57, 59, 63, 64, 66, 70, 71, 73, 77, 78, 80, 84, 85, 87, 91, 92, 94, 98, 99, 101, 105, 106, 108, 112, 113, 115, 119, 120, 122, 126, 127, 129, 133, 134, 136, 140 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1). FORMULA Partial sums of (0, 1, 2, 4, 1, 2, 4, 1, 2, 4, ...). - Gary W. Adamson, Jun 19 2008 G.f.: x^2*(1+2*x+4*x^2)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Dec 04 2011 From Wesley Ivan Hurt, Jun 08 2016: (Start) a(n) = a(n-1) + a(n-3) - a(n-4) for n>4. a(n) = (21*n-30-6*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9. a(3k) = 7k-4, a(3k-1) = 7k-6, a(3k-2) = 7k-7. (End) MAPLE A047357:=n->(21*n-30-6*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047357(n), n=1..100); # Wesley Ivan Hurt, Jun 08 2016 MATHEMATICA Select[Range[0, 200], Mod[#, 7] == 0 || Mod[#, 7] == 1 || Mod[#, 7] == 3 &] (* Vladimir Joseph Stephan Orlovsky, Jul 10 2011 *) Select[Range[0, 200], MemberQ[{0, 1, 3}, Mod[#, 7]]&] (* Harvey P. Dale, Nov 30 2012 *) PROG (MAGMA) [n : n in [0..150] | n mod 7 in [0, 1, 3]]; // Wesley Ivan Hurt, Jun 08 2016 CROSSREFS Cf. A047360. Sequence in context: A276002 A089970 A019270 * A003607 A087859 A300082 Adjacent sequences:  A047354 A047355 A047356 * A047358 A047359 A047360 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified September 25 06:05 EDT 2020. Contains 337335 sequences. (Running on oeis4.)