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%I A117719 #7 Jul 23 2023 20:15:39
%S A117719 1,2,5,11,29,64,169,373,985,2174,5741,12671,33461,73852,195025,430441,
%T A117719 1136689,2508794,6625109,14622323,38613965,85225144,225058681,
%U A117719 496728541,1311738121,2895146102,7645370045,16874148071,44560482149
%N A117719 a(2n) = A001653(n) (Numbers n such that 2*n^2 - 1 is a square), a(2n+1) = A038725(n+1).
%H A117719 G. C. Greubel, <a href="/A117719/b117719.txt">Table of n, a(n) for n = 0..1000</a>
%H A117719 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,6,0,-1).
%F A117719 G.f.: (1+2*x-x^2-x^3)/((1-2*x-x^2)*(1+2*x-x^2)).
%F A117719 a(n) = (1/4)*( 3*P(n+1) + 2*P(n) + (-1)^n*P(n-1) ), where P(n) = A000129(n). - _G. C. Greubel_, Jul 23 2023
%t A117719 LinearRecurrence[{0,6,0,-1}, {1,2,5,11}, 40] (* _G. C. Greubel_, Jul 23 2023 *)
%o A117719 (Magma) I:= [1,2,5,11]; [n le 4 select I[n] else 6*Self(n-2) -Self(n-4): n in [1..40]]; // _G. C. Greubel_, Jul 23 2023
%o A117719 (SageMath)
%o A117719 A000129=BinaryRecurrenceSequence(2,1,0,1)
%o A117719 def A117719(n): return (3*A000129(n+1) +2*A000129(n) +(-1)^n*A000129(n-1))/4
%o A117719 [A117719(n) for n in range(41)] # _G. C. Greubel_, Jul 23 2023
%Y A117719 Cf. A000129, A001653, A038725.
%K A117719 nonn,easy
%O A117719 0,2
%A A117719 _Creighton Dement_, Apr 13 2006

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