cp's OEIS Frontend

A344036 Number of degree n polynomials f(x) with coefficients 0 or 1 with the property that the thickness of x*f(x)+1 is greater than the thickness of f(x).

%I A344036 #41 Jul 08 2021 05:11:04
%S A344036 1,2,2,5,8,20,30,69,115,270,459,1036,1754,4027,6812,15447,26770,60187,
%T A344036 105107,234944,413964,921296,1633724,3610032,6458525,14220580,
%U A344036 25556634,56006901,101271220,220941515,401379967,872910068,1592208078,3452735767,6321260916,13659455014
%N A344036 Number of degree n polynomials f(x) with coefficients 0 or 1 with the property that the thickness of x*f(x)+1 is greater than the thickness of f(x).
%C A344036 The thickness of a polynomial f(x) is the magnitude of the largest coefficient in the expansion of f(x)^2.
%C A344036 Is the limit a(n)/2^(n-1) defined? Is the limit nonzero?
%H A344036 Martin Ehrenstein, <a href="/A344036/b344036.txt">Table of n, a(n) for n = 0..42</a>
%e A344036 For n = 3, there are a(3) = 5 such polynomials:
%e A344036 f(x)              | th(f(x)) | th(x*f(x)+1)
%e A344036 ------------------+----------+-------------
%e A344036 1 + x + x^2 + x^3 | 4        | 5
%e A344036 1     + x^2 + x^3 | 2        | 4
%e A344036 1 + x       + x^3 | 2        | 3
%e A344036     x       + x^3 | 2        | 3
%e A344036               x^3 | 1        | 2
%Y A344036 Cf. A169950.
%K A344036 nonn
%O A344036 0,2
%A A344036 _Peter Kagey_, Jun 16 2021
%E A344036 Offset corrected and more terms added by _Martin Ehrenstein_, Jun 19 2021