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%I #10 Jul 14 2012 13:49:19
%S 5,29,109,305,701,1405,2549,4289,6805,10301,15005,21169,29069,39005,
%T 51301,66305,84389,105949,131405,161201,195805,235709,281429,333505,
%U 392501,459005,533629,617009,709805,812701,926405,1051649,1189189
%N Numbers generated by the Fibonacci polynomial x^4 + 3x^2 + 1.
%C Start with the Fibonacci polynomials of A011973 (see "examples") and put in appropriate exponents, e.g. {1,1} = x^2 + 1, the generator of A002522; {1,2} = x^3 + 2x, the generator of A054602; and to get the next polynomial, multiply by x and add the previous polynomial, such that the generator for A085151 = x^4 + 3x^2 + 1 = (x)(x^3+2x) + (x^2+1).
%F 1. x^4 + 3x^2 + 1 2. a(n) = n*A054602(n) + A002522(n) 3. a(n) = denominator of [n, n, n, n]; with numerator = A054602(n).
%F a(n)=A057721(n). [From _R. J. Mathar_, Sep 12 2008]
%e 1. a(2) = f(2) of x^4 + 3x^2 + 1 = 29
%e 2. a(2) = 29 = (2)A054602 + A002522(2) = (2)(12) + 5.
%e 3. [2,2,2,2] = 12/29; a(2) = 29, & 12 = A054602(2). Thus [n,n,n,n] = A054602(n)/A085151(n).
%t f[n_] := n^4 + 3n^2 + 1; Array[f, 33]
%Y Cf. A054602, A002522, A011973.
%K nonn
%O 1,1
%A _Gary W. Adamson_, Jun 21 2003
%E More terms from _Robert G. Wilson v_, Aug 06 2006
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