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A247518 a(n) = a(n-1) * (11*a(n-1) - 16*a(n-2)) / (a(n-1) + 10*a(n-2)) with a(1) = 1, a(2) = 2. 2

%I #18 May 13 2023 11:42:18

%S 1,2,1,-1,3,-21,651,11067,70091,230299,349163,20539,-31349,121307,

%T -1158869,314053499,3606200523,18517231899,49530502251,52454812347,

%U -20635376629,43663915099,-217519736917,3068771480059,127881095493451,1094857900300187,4611286015320811

%N a(n) = a(n-1) * (11*a(n-1) - 16*a(n-2)) / (a(n-1) + 10*a(n-2)) with a(1) = 1, a(2) = 2.

%H G. C. Greubel, <a href="/A247518/b247518.txt">Table of n, a(n) for n = 1..500</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (11,-66,264,-704,1024).

%F 0 = a(n)*(16*a(n+1) + 10*a(n+2)) + a(n+1)*(-11*a(n+1) + a(n+2)) for all n in Z.

%F a(n) = a(1-n) * 4^(2*n-1) for all n in Z.

%F a(n) = b(n+1) * b(n) * b(n-1) * b(n-2) for all n in Z where b = A247487.

%F From _Chai Wah Wu_, Jun 09 2022: (Start)

%F a(n) = 11*a(n-1) - 66*a(n-2) + 264*a(n-3) - 704*a(n-4) + 1024*a(n-5) for n > 5.

%F G.f.: x*(-256*x^4 + 144*x^3 - 45*x^2 + 9*x - 1)/((4*x - 1)*(16*x^2 - 6*x + 1)*(16*x^2 - x + 1)). (End)

%t RecurrenceTable[{a[n] == a[n - 1]*(11*a[n - 1] - 16*a[n - 2])/(a[n - 1] + 10*a[n - 2]), a[1] == 1, a[2] == 2}, a, {n, 1, 50}] (* _G. C. Greubel_, Aug 05 2018 *)

%t nxt[{a_,b_}]:={b, b (11b-16a)/(b+10a)}; NestList[nxt,{1,2},30][[;;,1]] (* _Harvey P. Dale_, May 13 2023 *)

%o (PARI) {a(n) = my(A, t=1); if( n<1, t = 4^(2*n - 1); n = 1-n); t * if( n<3, n, A = vector(n, k, k); for(k=3, n, A[k] = A[k-1] * (11*A[k-1] - 16*A[k-2]) / (A[k-1] + 10*A[k-2])); A[n])};

%o (Magma) I:=[1, 2]; [n le 2 select I[n] else Self(n-1)*(11*Self(n-1) - 16*Self(n-2))/(Self(n-1) + 10*Self(n-2)): n in [1..30]]; // _G. C. Greubel_, Aug 05 2018

%o (GAP) a:=[1,2];; for n in [3..30] do a[n]:=a[n-1]*(11*a[n-1]-16*a[n-2])/(a[n-1]+10*a[n-2]); od; a; # _Muniru A Asiru_, Aug 05 2018

%Y Cf. A247487.

%K sign,easy

%O 1,2

%A _Michael Somos_, Sep 18 2014

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)