A047331 - OEIS

%I #13 Sep 08 2022 08:44:57

%S 2,3,5,6,9,10,12,13,16,17,19,20,23,24,26,27,30,31,33,34,37,38,40,41,

%T 44,45,47,48,51,52,54,55,58,59,61,62,65,66,68,69,72,73,75,76,79,80,82,

%U 83,86,87,89,90,93,94,96,97,100,101,103,104,107,108,110,111

%N Numbers that are congruent to {2, 3, 5, 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+x+2*x^2+x^3+x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - _R. J. Mathar_, Dec 04 2011

%F From _Wesley Ivan Hurt_, Jun 03 2016: (Start)

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

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

%F a(2k) = A047280(k), a(2k-1) = A047385(k). (End)

%p A047331:=n->(14*n-3-3*I^(2*n)-(1-I)*I^(-n)-(1+I)*I^n)/8: seq(A047331(n), n=1..100); # _Wesley Ivan Hurt_, Jun 03 2016

%t Table[(14n-3-3*I^(2n)-(1-I)*I^(-n)-(1+I)*I^n)/8, {n, 80}] (* _Wesley Ivan Hurt_, Jun 03 2016 *)

%o (Magma) [n : n in [0..150] | n mod 7 in [2, 3, 5, 6]]; // _Wesley Ivan Hurt_, Jun 03 2016

%Y Cf. A047280, A047385.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_