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).

1, 2, 2, 5, 8, 20, 30, 69, 115, 270, 459, 1036, 1754, 4027, 6812, 15447, 26770, 60187, 105107, 234944, 413964, 921296, 1633724, 3610032, 6458525, 14220580, 25556634, 56006901, 101271220, 220941515, 401379967, 872910068, 1592208078, 3452735767, 6321260916, 13659455014

Offset: 0

Author

Peter Kagey, Jun 16 2021

Keywords

• nonn

Comments

The thickness of a polynomial f(x) is the magnitude of the largest coefficient in the expansion of f(x)^2.

Is the limit a(n)/2^(n-1) defined? Is the limit nonzero?

Examples

			For n = 3, there are a(3) = 5 such polynomials:
f(x)              | th(f(x)) | th(x*f(x)+1)
------------------+----------+-------------
1 + x + x^2 + x^3 | 4        | 5
1     + x^2 + x^3 | 2        | 4
1 + x       + x^3 | 2        | 3
    x       + x^3 | 2        | 3
              x^3 | 1        | 2
		

Links

• Martin Ehrenstein, Table of n, a(n) for n = 0..42

Crossrefs

Cf. A169950.

Extensions

Offset corrected and more terms added by Martin Ehrenstein, Jun 19 2021