A364314 Number of polynomials (with nonnegative coefficients) of Cantor's height n and degree k (in the range {1, 2, ..., n-1}), for n >= 2; and for n = 1 the degree is k = 1.

1, 1, 3, 5, 14, 26, 57

Offset

1,3

Comments

For details on the recorded integer polynomials and their coefficients see A364312.

Links

Table of n, a(n) for n=1..7.

Example

a(3) = 3 because the coefficients in A364312 are [2, 1], [1, 2], for
 degree k = 1, and [1, 0, 1], for degree k = 2, and the three polynomials are 2*x + 1, x + 2, and x^2 + 1.
For the counting of algebraic numbers one also has to use the signed versions with leading sign +, and consider only irreducible polynomials. Therefore, if only real algebraic numbers are considered, [1, 0, 1] does not qualify, because it leads to a pair of complex conjugate roots, and the signed version [1, 0, -1] gives a reducible polynomial.

Crossrefs

Cf. A364312, A364313.

Sequence in context: A372436 A295359 A104208 * A026777 A007136 A145974

Adjacent sequences: A364311 A364312 A364313 * A364315 A364316 A364317

Keyword

nonn,more

Author

Wolfdieter Lang, Jul 19 2023

Status

approved