A084117 Multiplicity of the factor (1+x+x^2) in the characteristic polynomial modulo 2 of the symmetric matrix with entries binomial(i+j,i), 0<=i,j<n.

0, 0, 1, 0, 1, 0, 3, 2, 3, 2, 5, 0, 3, 2, 5, 4, 5, 4, 7, 2, 5, 0, 11, 6, 9, 8, 11, 6, 9, 8, 11, 10, 11, 10, 13, 8, 11, 6, 17, 12, 15, 10, 21, 0, 11, 6, 17, 12, 15, 14, 17, 12, 15, 10, 21, 16, 19, 18, 21, 16, 19, 18, 21, 20, 21, 20, 23, 18, 21, 16, 27, 22, 25, 20, 31, 10, 21, 16, 27, 22, 25

Offset

0,7

Links

Table of n, a(n) for n=0..80.

Roland Bacher and R. Chapman, Symmetric Pascal matrices modulo p, European J. Combin. 25 (2004), no. 4, 459-473.

Formula

a(2n) = n - a(n). - Ralf Stephan, Oct 07 2003

a(n) = (n - A085015(n))/2. See Theorem 1.4 of Bacher and Chapman. - Michel Marcus, Dec 13 2025

Crossrefs

Cf. A085015.

Sequence in context: A093489 A066919 A268714 * A116895 A134267 A249800

Adjacent sequences: A084114 A084115 A084116 * A084118 A084119 A084120

Keyword

easy,nonn

Author

Roland Bacher, Jun 18 2003

Status

approved