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%I #36 Oct 04 2023 11:03:14
%S 0,1,2,4,5,7,8,9,11,12,14,15,16,18,19,21,22,23,25,26,28,29,30,32,33,
%T 35,36,37,39,40,42,43,44,46,47,49,50,51,53,54,56,57,58,60,61,63,64,65,
%U 67,68,70,71,72,74,75,77,78
%N Numbers that are congruent to {0, 1, 2, 4, 5} mod 7.
%H Vincenzo Librandi, <a href="/A047381/b047381.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1)
%F a(n) = floor( (7/5)(n-1) ). [_Gary Detlefs_, Feb 20 2010]
%F From _R. J. Mathar_, Mar 11 2011: (Start)
%F a(n) = a(n-1) + a(n-5) - a(n-6).
%F G.f.: x^2*(1 + x + 2*x^2 + x^3 + 2*x^4) / ((x^4 + x^3 + x^2 + x + 1)*(x-1)^2). (End)
%F 5*a(n) = 7*n-9-b(n) where b(n) = b(n-5) = 1, -2, 0, 2, -1 (for offset 0). - _R. J. Mathar_, Jul 22 2020
%p seq(floor((7/5)*(n-1)),n=1..56); # _Gary Detlefs_, Feb 20 2010
%t CoefficientList[Series[x (1 + x + 2 x^2 + x^3 + 2 x^4) / ((x^4 + x^3 + x^2 + x + 1) (x - 1)^2), {x, 0, 60}], x] (* _Vincenzo Librandi_, Jul 26 2013 *)
%t LinearRecurrence[{1,0,0,0,1,-1},{0,1,2,4,5,7},80] (* _Harvey P. Dale_, Oct 04 2023 *)
%o (Magma) [ n: n in [1..80] | n mod 7 in [0,1,2,4,5] ]; // _Vincenzo Librandi_, Jul 26 2013
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_
%E Formula and Maple code adapted to the offset by _Wesley Ivan Hurt_, Jul 16 2013
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