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.

1, 2, 1, -1, 3, -21, 651, 11067, 70091, 230299, 349163, 20539, -31349, 121307, -1158869, 314053499, 3606200523, 18517231899, 49530502251, 52454812347, -20635376629, 43663915099, -217519736917, 3068771480059, 127881095493451, 1094857900300187, 4611286015320811

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..500

Index entries for linear recurrences with constant coefficients, signature (11,-66,264,-704,1024).

Formula

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.

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

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

From Chai Wah Wu, Jun 09 2022: (Start)

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.

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)

Mathematica

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

Prog

(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])};
(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
(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

Crossrefs

Cf. A247487.

Sequence in context: A134357 A049258 A228832 * A078076 A010247 A087605

Adjacent sequences: A247515 A247516 A247517 * A247519 A247520 A247521

Keyword

sign,easy

Author

Michael Somos, Sep 18 2014

Status

approved