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A192802 Coefficient of x in the reduction of the polynomial (x+2)^n by x^3->x^2+x+1.

%I A192802 #21 Feb 18 2025 08:59:24
%S A192802 0,1,4,13,42,143,514,1915,7268,27805,106680,409633,1573086,6040587,
%T A192802 23193782,89051615,341901032,1312664601,5039704492,19348873781,
%U A192802 74285859698,285204660583,1094982340202,4203950929347,16140172668812
%N A192802 Coefficient of x in the reduction of the polynomial  (x+2)^n by x^3->x^2+x+1.
%C A192802 For discussions of polynomial reduction, see A192232 and A192744.
%H A192802 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-15,11).
%F A192802 a(n) = 7*a(n-1)-15*a(n-2)+11*a(n-3).
%F A192802 G.f.: x*(3*x-1)/(11*x^3-15*x^2+7*x-1). - _Colin Barker_, Jul 27 2012
%e A192802 The first five polynomials p(n,x) and their reductions:
%e A192802 p(1,x)=1 -> 1
%e A192802 p(2,x)=x+2 -> x+2
%e A192802 p(3,x)=x^2+4x+4 -> x^2+1
%e A192802 p(4,x)=x^3+6x^2+12x+8 -> x^2+4x+4
%e A192802 p(5,x)=x^4+8x^3+24x^2+32x+16 -> 7x^2+13*x+9, so that
%e A192802 A192798=(1,2,4,9,25,...), A192799=(0,1,4,13,42,...), A192800=(0,0,1,7,34,...).
%t A192802 (See A192801.)
%t A192802 LinearRecurrence[{7,-15,11},{0,1,4},30] (* _Harvey P. Dale_, Nov 05 2015 *)
%Y A192802 Cf. A192744, A192232, A192801, A192803.
%K A192802 nonn,easy
%O A192802 0,3
%A A192802 _Clark Kimberling_, Jul 10 2011
%E A192802 Recurrence corrected by _Colin Barker_, Jul 27 2012