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

0,2

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?

Links

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

Example

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

Crossrefs

Cf. A169950.

Sequence in context: A337079 A095005 A209066 * A208938 A019086 A076949

Adjacent sequences: A344033 A344034 A344035 * A344037 A344038 A344039

Keyword

nonn

Author

Peter Kagey, Jun 16 2021

Extensions

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

Status

approved