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A192779
Coefficient of x^2 in the reduction of the n-th Fibonacci polynomial by x^3->x^2+3x+1.
6
0, 0, 1, 1, 7, 12, 47, 107, 337, 868, 2520, 6808, 19192, 52756, 147185, 407069, 1131599, 3136292, 8707655, 24151335, 67025633, 185946904, 515971328, 1431563056, 3972149312, 11021051864, 30579529249, 84846231017, 235416993159, 653192251196
OFFSET
1,5
COMMENTS
For discussions of polynomial reduction, see A192232 and A192744.
FORMULA
a(n) = a(n-1)+6*a(n-2)-a(n-3)-6*a(n-4)+a(n-5)+a(n-6).
G.f.: -x^3/((x^2-x-1)*(x^4+2*x^3-3*x^2-2*x+1)). [Colin Barker, Nov 23 2012]
EXAMPLE
The first five polynomials p(n,x) and their reductions:
F1(x)=1 -> 1
F2(x)=x -> x
F3(x)=x^2+1 -> x^2+1
F4(x)=x^3+2x -> x^2+5x+1
F5(x)=x^4+3x^2+1 -> 7x^2+4x+2, so that
A192777=(1,0,1,1,2,...), A192778=(0,1,0,5,4,...), A192779=(0,0,1,1,7,...)
MATHEMATICA
(See A192777.)
LinearRecurrence[{1, 6, -1, -6, 1, 1}, {0, 0, 1, 1, 7, 12}, 30] (* Harvey P. Dale, Oct 29 2018 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 09 2011
STATUS
approved