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%I #24 Sep 08 2022 08:45:57
%S 1,9,17,3,11,19,5,13,21,7,15,23,9,17,25,11,19,27,13,21,29,15,23,31,17,
%T 25,33,19,27,35,21,29,37,23,31,39,25,33,41,27,35,43,29,37,45,31,39,47,
%U 33,41,49,35,43,51,37,45,53,39,47,55,41,49,57,43,51,59
%N a(1) = 1, a(2) = 9, a(3) = 17; for n>3, a(n) = a(n-3) + 2.
%D Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 62.
%H Andrew Howroyd, <a href="/A190322/b190322.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F a(1)=1, a(2)=9, a(3)=17, a(4)=3, a(n) = a(n-1)+a(n-3)-a(n-4). - _Harvey P. Dale_, Feb 24 2014
%F G.f.: x*(1+8*x+8*x^2-15*x^3) / ((x-1)^2*(x^2+x+1)). - _Colin Barker_, Sep 12 2014
%t RecurrenceTable[{a[1]==1,a[2]==9,a[3]==17,a[n]==a[n-3]+2},a,{n,70}] (* or *) LinearRecurrence[{1,0,1,-1},{1,9,17,3},70] (* _Harvey P. Dale_, Feb 24 2014 *)
%o (PARI) Vec(-x*(15*x^3-8*x^2-8*x-1)/((x-1)^2*(x^2+x+1)) + O(x^100)) \\ _Colin Barker_, Sep 12 2014
%o (Magma) I:=[1, 9, 17, 3]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..30]]; // _G. C. Greubel_, Dec 30 2017
%Y Cf. A136313.
%K nonn,easy
%O 1,2
%A _Nathaniel Johnston_, May 08 2011
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