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 A076844 a(1) = a(2) = a(3) = 1; a(n) = (a(n-1) + a(n-2) + 1)/a(n-3) (for n>3). 5

%I

%S 1,1,1,3,5,9,5,3,1,1,1,3,5,9,5,3,1,1,1,3,5,9,5,3,1,1,1,3,5,9,5,3,1,1,

%T 1,3,5,9,5,3,1,1,1,3,5,9,5,3,1,1,1,3,5,9,5,3,1,1,1,3,5,9,5,3,1,1,1,3,

%U 5,9,5,3,1,1,1,3,5,9,5,3,1,1,1,3,5,9,5,3,1,1,1,3,5,9,5,3,1,1,1,3,5,9,5,3,1

%N a(1) = a(2) = a(3) = 1; a(n) = (a(n-1) + a(n-2) + 1)/a(n-3) (for n>3).

%C Any sequence a(1),a(2),a(3),... defined by the recurrence a(n) = (a(n-1) + a(n-2) + 1)/a(n-3) (for n>3) has period 8. - _James Propp_, Nov 20 2002

%C Terms of the simple continued fraction of 778/(sqrt(2223933)-995). - _Paolo P. Lava_, Aug 06 2009

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 1).

%F a(n) = 1/8*(3*(n mod 8) + 3*((n+1) mod 8) + 5*((n+2) mod 8) - 3*((n+3) mod 8) - ((n+4) mod 8) - ((n+5) mod 8) + ((n+6) mod 8) + ((n+7) mod 8)) with n>=0. - _Paolo P. Lava_, Nov 27 2006

%p a := 1; b := 1; c := 1; f := proc(n) option remember; global a,b,c; if n=1 then RETURN(a); fi; if n=2 then RETURN(b); fi; if n=3 then RETURN(c); fi; RETURN((f(n-1)+f(n-2)+1)/f(n-3)); end;

%t nxt[{a_,b_,c_}]:={b,c,(b+c+1)/a}; Transpose[NestList[nxt,{1,1,1},110]][[1]] (* or *) PadRight[{},110,{1,1,1,3,5,9,5,3}] (* _Harvey P. Dale_, Jan 13 2015 *)

%t LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1},{1, 1, 1, 3, 5, 9, 5, 3},105] (* _Ray Chandler_, Aug 25 2015 *)

%Y Cf. A076840, A076841, A076839, A076842, A076843.

%K nonn

%O 1,4

%A _N. J. A. Sloane_, Nov 21 2002

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Last modified September 16 08:36 EDT 2019. Contains 327091 sequences. (Running on oeis4.)