A192473 - OEIS

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A192473

Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x)=1+x^n+x^(2n+2).

4, 9, 23, 58, 149, 385, 1000, 2605, 6799, 17766, 46457, 121537, 318044, 832417, 2178919, 5703874, 14931949, 39090753, 102338336, 267921061, 701419679, 1836329614, 4807555633, 12586315393, 32951355124, 86267692665, 225851630135

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OFFSET

1,1

COMMENTS

For an introduction to reductions of polynomials by substitutions such as x^2->x+1, see A192232.

LINKS

Table of n, a(n) for n=1..27.

FORMULA

Conjectures from Colin Barker, Jun 07 2019: (Start)

G.f.: x*(4 - 7*x - x^2 + x^3) / ((1 - 3*x + x^2)*(1 - x - x^2)).

a(n) = 4*a(n-1) - 3*a(n-2) - 2*a(n-3) + a(n-4) for n>4.

(End)