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Numbers that are congruent to {1, 2, 4, 5} mod 7.
6

%I #29 Dec 25 2023 13:46:27

%S 1,2,4,5,8,9,11,12,15,16,18,19,22,23,25,26,29,30,32,33,36,37,39,40,43,

%T 44,46,47,50,51,53,54,57,58,60,61,64,65,67,68,71,72,74,75,78,79,81,82,

%U 85,86,88,89,92,93,95,96,99,100,102,103,106,107,109,110

%N Numbers that are congruent to {1, 2, 4, 5} 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*(1+x+2*x^2+x^3+2*x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Oct 08 2011

%F From _Wesley Ivan Hurt_, May 20 2016: (Start)

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

%F a(n) = (14*n - 11 - 3*i^(2*n) - (1+i)*i^(-n-1) - (1-i)*i^(n+1))/8 where i=sqrt(-1).

%F a(2n) = A047385(n), a(2n-1) = A047346(n). (End)

%p A047380:=n->(14*n-11-3*I^(2*n)-(1+I)*I^(-n-1)-(1-I)*I^(n+1))/8: seq(A047380(n), n=1..100); # _Wesley Ivan Hurt_, May 20 2016

%t Table[(14n-11-3I^(2n)-(1+I)I^(-n-1)-(1-I)I^(n+1))/8, {n, 80}] (* _Wesley Ivan Hurt_, May 20 2016 *)

%t LinearRecurrence[{1,0,0,1,-1},{1,2,4,5,8},100] (* _Harvey P. Dale_, Jun 05 2016 *)

%o (PARI) a(n)=(n-1)\4*7+[5,1,2,4][n%4+1] \\ _Charles R Greathouse IV_, Jun 11 2015

%Y Cf. A002265, A047346, A047385.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_