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Pisot sequence T(4,7).
1

%I #24 Mar 22 2016 15:21:54

%S 4,7,12,20,33,54,88,143,232,376,609,986,1596,2583,4180,6764,10945,

%T 17710,28656,46367,75024,121392,196417,317810,514228,832039,1346268,

%U 2178308,3524577,5702886,9227464,14930351,24157816,39088168,63245985,102334154,165580140

%N Pisot sequence T(4,7).

%H Colin Barker, <a href="/A020732/b020732.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1).

%F a(n) = Fibonacci(n+5) - 1.

%F a(n) = 2*a(n-1) - a(n-3).

%F From _Colin Barker_, Mar 22 2016: (Start)

%F a(n) = (-1+(2^(-1-n)*((1-sqrt(5))^n*(-11+5*sqrt(5))+(1+sqrt(5))^n*(11+5*sqrt(5))))/sqrt(5)).

%F G.f.: (4-x-2*x^2) / ((1-x)*(1-x-x^2)).

%F (End)

%t Join[{a=4,b=7},Table[c=a+b+1;a=b;b=c,{n,0,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Nov 22 2010 *)

%o (PARI) Vec((4-x-2*x^2)/((1-x)*(1-x-x^2)) + O(x^50)) \\ _Colin Barker_, Mar 22 2016

%Y Subsequence of A000071. See A008776 for definitions of Pisot sequences.

%K nonn,easy

%O 0,1

%A _David W. Wilson_