A085151 Numbers generated by the Fibonacci polynomial x^4 + 3x^2 + 1.

5, 29, 109, 305, 701, 1405, 2549, 4289, 6805, 10301, 15005, 21169, 29069, 39005, 51301, 66305, 84389, 105949, 131405, 161201, 195805, 235709, 281429, 333505, 392501, 459005, 533629, 617009, 709805, 812701, 926405, 1051649, 1189189

Offset

1,1

Comments

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).

Links

Table of n, a(n) for n=1..33.

Formula

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).

a(n)=A057721(n). [From R. J. Mathar, Sep 12 2008]

Example

1. a(2) = f(2) of x^4 + 3x^2 + 1 = 29
2. a(2) = 29 = (2)A054602 + A002522(2) = (2)(12) + 5.
3. [2,2,2,2] = 12/29; a(2) = 29, & 12 = A054602(2). Thus [n,n,n,n] = A054602(n)/A085151(n).

Mathematica

f[n_] := n^4 + 3n^2 + 1; Array[f, 33]

Crossrefs

Cf. A054602, A002522, A011973.

Sequence in context: A153076 A034700 A057721 * A119494 A334544 A268929

Adjacent sequences: A085148 A085149 A085150 * A085152 A085153 A085154

Keyword

nonn

Author

Gary W. Adamson, Jun 21 2003

Extensions

More terms from Robert G. Wilson v, Aug 06 2006

Status

approved