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 A047297 Numbers that are congruent to {0, 3, 4, 6} mod 7. 1

%I

%S 0,3,4,6,7,10,11,13,14,17,18,20,21,24,25,27,28,31,32,34,35,38,39,41,

%T 42,45,46,48,49,52,53,55,56,59,60,62,63,66,67,69,70,73,74,76,77,80,81,

%U 83,84,87,88,90,91,94,95,97,98,101,102,104,105,108,109,111

%N Numbers that are congruent to {0, 3, 4, 6} mod 7.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).

%F G.f.: x^2*(3+x+2*x^2+x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - _R. J. Mathar_, Oct 25 2011

%F From _Wesley Ivan Hurt_, Jun 02 2016: (Start)

%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

%F a(n) = (14*n-9+3*i^(2*n)-(1+i)*i^(-n)-(1-i)*i^n)/8 where i=sqrt(-1).

%F a(2k) = A047280(k), a(2k-1) = A047345(k). (End)

%p A047297:=n->(14*n-9+3*I^(2*n)-(1+I)*I^(-n)-(1-I)*I^n)/8: seq(A047297(n), n=1..100); # _Wesley Ivan Hurt_, Jun 02 2016

%t Table[(14n-9+3*I^(2n)-(1+I)*I^(-n)-(1-I)*I^n)/8, {n, 80}] (* _Wesley Ivan Hurt_, Jun 02 2016 *)

%o (MAGMA) [n : n in [0..150] | n mod 7 in [0, 3, 4, 6]]; // _Wesley Ivan Hurt_, Jun 02 2016

%Y Cf. A047280, A047345.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_

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Last modified May 12 07:28 EDT 2021. Contains 343821 sequences. (Running on oeis4.)