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A055271 a(n) = 5a(n-1) - a(n-2); a(0)=1, a(1)=7. 3

%I

%S 1,7,34,163,781,3742,17929,85903,411586,1972027,9448549,45270718,

%T 216905041,1039254487,4979367394,23857582483,114308545021,

%U 547685142622,2624117168089,12572900697823,60240386321026,288629030907307

%N a(n) = 5a(n-1) - a(n-2); a(0)=1, a(1)=7.

%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 122-125, 194-196.

%H I. Adler, <a href="http://www.fq.math.ca/Scanned/7-2/adler.pdf">Three Diophantine equations - Part II</a>, Fib. Quart., 7 (1969), pp. 181-193.

%H E. I. Emerson, <a href="http://www.fq.math.ca/Scanned/7-3/emerson.pdf">Recurrent Sequences in the Equation DQ^2=R^2+N</a>, Fib. Quart., 7 (1969), pp. 231-242.

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-1).

%F a(n) = (7*(((5+sqrt(21))/2)^n - ((5-sqrt(21))/2)^n) - (((5+sqrt(21))/2)^(n-1) - ((5-sqrt(21))/2)^(n-1)))/sqrt(21).

%F G.f.: (1+2*x)/(1-5*x+x^2).

%F a(n) = (-1)^n*Sum_{k = 0..n} A238731(n,k)*(-8)^k. - _Philippe Deléham_, Mar 05 2014

%Y Cf. A030221.

%K easy,nonn

%O 0,2

%A _Barry E. Williams_, May 10 2000

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Last modified July 18 15:37 EDT 2019. Contains 325144 sequences. (Running on oeis4.)