cp's OEIS Frontend

A192473 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x)=1+x^n+x^(2n+2).

%I A192473 #8 Jun 07 2019 22:02:01
%S A192473 4,9,23,58,149,385,1000,2605,6799,17766,46457,121537,318044,832417,
%T A192473 2178919,5703874,14931949,39090753,102338336,267921061,701419679,
%U A192473 1836329614,4807555633,12586315393,32951355124,86267692665,225851630135
%N A192473 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x)=1+x^n+x^(2n+2).
%C A192473 For an introduction to reductions of polynomials by substitutions such as x^2->x+1, see A192232.
%F A192473 Conjectures from _Colin Barker_, Jun 07 2019: (Start)
%F A192473 G.f.: x*(4 - 7*x - x^2 + x^3) / ((1 - 3*x + x^2)*(1 - x - x^2)).
%F A192473 a(n) = 4*a(n-1) - 3*a(n-2) - 2*a(n-3) + a(n-4) for n>4.
%F A192473 (End)
%e A192473 The first four polynomials p(n,x) and their reductions are as follows:
%e A192473 p(1,x)=1+x+x^4 -> 3+4x
%e A192473 p(2,x)=1+x^2+x^6 -> 7+9x
%e A192473 p(3,x)=1+x^3+x^8 -> 15+23x
%e A192473 p(4,x)=1+x^4+x^10 -> 37+58x.
%e A192473 From these, read
%e A192473 A192472=(3,7,15,37,...) and A192473=(4,9,23,58,...)
%t A192473 (See A192472.)
%Y A192473 Cf. A192232, A192472.
%K A192473 nonn
%O A192473 1,1
%A A192473 _Clark Kimberling_, Jul 01 2011