A364313 Length of row n of the irregular triangle A364312.

2, 2, 7, 13, 44, 95, 231

Offset: 1

Author

Wolfdieter Lang, Jul 19 2023

Keywords

• nonn
• more

Comments

This gives the total number a(n) of nonnegative coefficients of the integer polynomials of degree k = 1, 2, ..., n-1 of Cantor's height n, for n >= 2, and for n = 1 the degree is k = 1, with polynomial 1*x.

Not all rows of A364312 have entries for k = n-1, e.g., for n = 4 the k = 3 entry [1, 0, 0, 1] is not recorded because both x^3 + 1 and the signed version x^3 - 1 factorize. Similar cases appear for n = 6 and n = 7.

Examples

			a(3) = 7 because row n = 3 of A364312 is 2, 1, 1, 2, 1, 0, 1, from [2, 1], [1, 2]; [1, 0, 1] for the polynomials 2*x + 1, x + 2, x^2 + 1.
		

Crossrefs

Cf. A364312.