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A197916 Related to the periodic sequence A171654. 0

%I #19 Jul 30 2019 18:52:13

%S 0,1,6,7,2,3,8,9,4,5,10,11,6,7,12,13,8,9,14,15,10,11,16,17,12,13,18,

%T 19,14,15,20,21,16,17,22,23,18,19,24,25,20,21,26,27,22,23,28,29,24,25,

%U 30,31,26,27,32,33,28,29,34,35,30,31,36,37,32,33,38,39

%N Related to the periodic sequence A171654.

%C All numbers appear twice except numbers 0,1,2,3,4,5 which appear once. - From A. Salagnad, Oct 19 2011.

%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)=A171654(n) mod 10.

%F a(n)=Sum_k>=0 {A030308(n,k)*b(k)} with b(0)=1, b(1)=6 and b(k)=2^(k-1) for k>1.

%F G.f. ( -x*(-1-5*x-x^2+5*x^3) ) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 20 2011

%F a(n) = n/2+(11-(-1)^n)/4 -5*A057077(n)/2. - R. J. Mathar, Oct 20 2011

%t LinearRecurrence[{1,0,0,1,-1},{0,1,6,7,2},80] (* _Harvey P. Dale_, Jul 30 2019 *)

%o (PARI) a(n)=([0,1,0,0,0; 0,0,1,0,0; 0,0,0,1,0; 0,0,0,0,1; -1,1,0,0,1]^n*[0;1;6;7;2])[1,1] \\ _Charles R Greathouse IV_, Jul 06 2017

%Y Cf. A171654.

%K easy,nonn

%O 0,3

%A _Philippe Deléham_, Oct 19 2011

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)