cp's OEIS Frontend

A192803 Coefficient of x^2 in the reduction of the polynomial (x+2)^n by x^3->x^2+x+1.

%I A192803 #18 Feb 18 2025 03:55:11
%S A192803 0,0,1,7,34,144,575,2239,8632,33164,127297,488571,1875346,7199124,
%T A192803 27637959,106107659,407374592,1564024808,6004739025,23053921567,
%U A192803 88510638482,339817775144,1304657986015,5008956298247,19230819824088,73832632141076
%N A192803 Coefficient of x^2 in the reduction of the polynomial (x+2)^n by x^3->x^2+x+1.
%C A192803 For discussions of polynomial reduction, see A192232 and A192744.
%H A192803 J. Pan, <a href="https://cs.uwaterloo.ca/journals/JIS/OL13/Pan/pan8.html">Multiple Binomial Transforms and Families of Integer Sequences </a>, J. Int. Seq. 13 (2010), 10.4.2, T^(2).
%H A192803 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-15,11).
%F A192803 a(n) = 7*a(n-1)-15*a(n-2)+11*a(n-3).
%F A192803 G.f.: -x^2/(11*x^3-15*x^2+7*x-1). [_Colin Barker_, Jul 27 2012]
%e A192803 The first five polynomials p(n,x) and their reductions:
%e A192803 p(1,x)=1 -> 1
%e A192803 p(2,x)=x+2 -> x+2
%e A192803 p(3,x)=x^2+4x+4 -> x^2+1
%e A192803 p(4,x)=x^3+6x^2+12x+8 -> x^2+4x+4
%e A192803 p(5,x)=x^4+8x^3+24x^2+32x+16 -> 7x^2+13*x+9, so that
%e A192803 A192798=(1,2,4,9,25,...), A192799=(0,1,4,13,42,...), A192800=(0,0,1,7,34,...).
%t A192803 (See A192801.)
%Y A192803 Cf. A192744, A192232, A192616, A192801, A192802.
%K A192803 nonn,easy
%O A192803 0,4
%A A192803 _Clark Kimberling_, Jul 10 2011
%E A192803 Recurrence corrected by _Colin Barker_, Jul 27 2012