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A163302 Duplicate of A084057. 1
1, 6, 16, 56, 176, 576, 1856, 6016, 19456, 62976, 203776, 659456, 2134016, 6905856, 22347776, 72318976, 234029056, 757334016, 2450784256, 7930904576, 25664946176, 83053510656, 268766806016, 869747654656, 2814562533376, 9108115685376, 29474481504256 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For denominators, see A063727, which are the product of the powers of 2 and the Fibonacci sequence.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

FORMULA

Reciprocal formula: a(n)=(a(n-1)+1)/(c*a(n-1)), with a(1)=1. (Reversed formula for accelerated approximation of Phi: a'(n)=(a(n-1)+1)/(a(n-1)+c); a'(n)=(c*a(n-1))/(a(n-1)+1), with c=2.) - Mark Dols, Jul 28 2009]

G.f. and recurrence: x*(1+4*x)/(1-2*x-4*x^2), a(n)=2*a(n-1)+4*a(n-2). - Colin Barker, Feb 08 2012

G.f.: G(0)/(2*x)-1/x, where G(k)= 1 + 1/(1 - x*(5*k-1)/(x*(5*k+4) - 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 04 2013

a(n) = A084057(n). - Vaclav Kotesovec, Mar 10 2014

MATHEMATICA

CoefficientList[Series[(1 + 4 x)/(1 - 2 x - 4 x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 12 2014 *)

PROG

(MAGMA) I:=[1, 6]; [n le 2 select I[n] else 2*Self(n-1)+4*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Mar 12 2014

CROSSREFS

Cf. A000032, A000079, A084057, A063727, A000045

Sequence in context: A192000 A032282 A084057 * A223028 A091649 A125628

Adjacent sequences:  A163299 A163300 A163301 * A163303 A163304 A163305

KEYWORD

dead

AUTHOR

Mark Dols, Jul 24 2009

STATUS

approved

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Last modified November 14 06:14 EST 2018. Contains 317162 sequences. (Running on oeis4.)