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 A047371 Numbers that are congruent to {0, 2, 3, 5} mod 7. 1

%I

%S 0,2,3,5,7,9,10,12,14,16,17,19,21,23,24,26,28,30,31,33,35,37,38,40,42,

%T 44,45,47,49,51,52,54,56,58,59,61,63,65,66,68,70,72,73,75,77,79,80,82,

%U 84,86,87,89,91,93,94,96,98,100,101,103,105,107,108,110

%N Numbers that are congruent to {0, 2, 3, 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 a(n) = floor((7n-6)/4). [_Gary Detlefs_, Mar 06 2010]

%F G.f.: x^2*(2+x+2*x^2+2*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 04 2011

%F From _Wesley Ivan Hurt_, Jun 04 2016: (Start)

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

%F a(n) = i^(-n)*((14*n-15)*i^n+i-1-(1+i)*i^(2*n)+i^(-n))/8 where i=sqrt(-1).

%F a(2k) = A047385(k), a(2k-1) = A047355(k). (End)

%F E.g.f.: (8 + sin(x) - cos(x) + (7*x - 8)*sinh(x) + 7*(x - 1)*cosh(x))/4. - _Ilya Gutkovskiy_, Jun 04 2016

%p seq(floor((7*n-6)/4), n=1..56); # [_Gary Detlefs_, Mar 06 2010]

%t Table[I^(-n)*((14n-15)*I^n+I-1-(1+I)*I^(2n)+I^(-n))/8, {n, 80}] (* _Wesley Ivan Hurt_, Jun 04 2016 *)

%t LinearRecurrence[{1,0,0,1,-1},{0,2,3,5,7},70] (* _Harvey P. Dale_, Oct 24 2018 *)

%o (MAGMA) [n : n in [0..150] | n mod 7 in [0, 2, 3, 5]]; // _Wesley Ivan Hurt_, Jun 04 2016

%Y Cf. A047355, A047385.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_

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Last modified July 31 22:33 EDT 2021. Contains 346377 sequences. (Running on oeis4.)