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 A047298 Numbers that are congruent to {1, 3, 4, 6} mod 7. 2
 1, 3, 4, 6, 8, 10, 11, 13, 15, 17, 18, 20, 22, 24, 25, 27, 29, 31, 32, 34, 36, 38, 39, 41, 43, 45, 46, 48, 50, 52, 53, 55, 57, 59, 60, 62, 64, 66, 67, 69, 71, 73, 74, 76, 78, 80, 81, 83, 85, 87, 88, 90, 92, 94, 95, 97, 99, 101, 102, 104, 106, 108, 109, 111 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1). FORMULA a(n) = ceiling(ceiling((7n + 2)/2)/2). G.f.: x*(1+2*x+x^2+2*x^3+x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011 From Wesley Ivan Hurt, May 22 2016: (Start) a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. a(n) = i^(-n)*(i-1-7*i^n+14*n*i^n-(1+i)*i^(2n)+i^(-n))/8 where i=sqrt(-1). a(2n) = A047280(n), a(2n-1) = A047346(n). (End) E.g.f.: (4 + sin(x) - cos(x) + (7*x - 4)*sinh(x) + (7*x - 3)*cosh(x))/4. - Ilya Gutkovskiy, May 23 2016 MAPLE A047298:=n->I^(-n)*(I-1-7*I^n+14*n*I^n-(1+I)*I^(2*n)+I^(-n))/8: seq(A047298(n), n=1..100); # Wesley Ivan Hurt, May 22 2016 MATHEMATICA Table[I^(-n)*(I-1-7I^n+14n*I^n-(1+I)*I^(2n)+I^(-n))/8, {n, 80}] (* Wesley Ivan Hurt, May 22 2016 *) LinearRecurrence[{1, 0, 0, 1, -1}, {1, 3, 4, 6, 8}, 80] (* Vincenzo Librandi, May 24 2016 *) PROG (MAGMA) [n : n in [0..150] | n mod 7 in [1, 3, 4, 6]]; // Wesley Ivan Hurt, May 22 2016 CROSSREFS Cf. A047280, A047346. Sequence in context: A003257 A184006 A187415 * A184748 A184742 A232499 Adjacent sequences:  A047295 A047296 A047297 * A047299 A047300 A047301 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Wesley Ivan Hurt, May 22 2016 STATUS approved

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Last modified May 18 11:30 EDT 2021. Contains 343995 sequences. (Running on oeis4.)