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 A047322 Numbers that are congruent to {0, 1, 5, 6} mod 7. 2
 0, 1, 5, 6, 7, 8, 12, 13, 14, 15, 19, 20, 21, 22, 26, 27, 28, 29, 33, 34, 35, 36, 40, 41, 42, 43, 47, 48, 49, 50, 54, 55, 56, 57, 61, 62, 63, 64, 68, 69, 70, 71, 75, 76, 77, 78, 82, 83, 84, 85, 89, 90, 91, 92, 96, 97, 98, 99, 103, 104, 105, 106, 110, 111 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 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+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=1, b(1)=5, b(k)=7*2^(k-2) for k>1. - Philippe Deléham, Oct 19 2011 G.f.: x^2*(1+4*x+x^2+x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 03 2011 From Wesley Ivan Hurt, May 23 2016: (Start) a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. a(n) = (14n-11-3*I^(2n)+(3-3*I)*I^(-n)+(3+3*I)*I^n)/8 where I=sqrt(-1). a(2n) = A047336(n), a(2n-1) = A047382(n). (End) E.g.f.: (4 - 3*sin(x) + 3*cos(x) + (7*x - 4)*sinh(x) + 7*(x - 1)*cosh(x))/4. - Ilya Gutkovskiy, May 24 2016 MAPLE A047322:=n->(14*n-11-3*I^(2*n)+(3-3*I)*I^(-n)+(3+3*I)*I^n)/8: seq(A047322(n), n=1..100); # Wesley Ivan Hurt, May 23 2016 MATHEMATICA Table[(14n-11-3*I^(2n)+(3-3*I)*I^(-n)+(3+3*I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, May 23 2016 *) LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 5, 6, 7}, 60] (* Vincenzo Librandi, May 24 2016 *) PROG (MAGMA) [n : n in [0..150] | n mod 7 in [0, 1, 5, 6]]; // Wesley Ivan Hurt, May 23 2016 CROSSREFS Cf. A030308, A047336, A047382. Sequence in context: A262513 A130206 A178502 * A236242 A309102 A080703 Adjacent sequences:  A047319 A047320 A047321 * A047323 A047324 A047325 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Wesley Ivan Hurt, May 23 2016 STATUS approved

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Last modified May 12 04:27 EDT 2021. Contains 343810 sequences. (Running on oeis4.)