A176296 Irregular triangle read by rows: eigenvalues of Laplacian of parity's landscape graph.

0, 2, 0, 4, 0, 6, 8, 0, 8, 12, 0, 10, 16, 18, 0, 12, 20, 24, 0, 14, 24, 30, 32, 0, 16, 28, 36, 40, 0, 18, 32, 42, 48, 50

Offset

1,2

Comments

Note similarity to Pascal's triangle. Starts with parity order k=2. Each row starts with zero. Second column=(k-1)*2. Third column=(k-2)*4. Fourth column=(k-3)*6. Eigenvalue multiplicities (not given) sum to 2^n for each row.

Largest value appears to be ceiling((k-1)(k+1)/2) but this is open.

Links

Table of n, a(n) for n=1..34.

W. B. Langdon, Elementary bit string mutation landscapes, Foundations of Genetic Algorithms XI, Proceedings, pp. 25-42.

Example

0, 2;
0, 4;
0, 6, 8;
0, 8, 12;
0, 10, 16, 18;
0, 12, 20, 24;
0, 14, 24, 30, 32;
0, 16, 28, 36, 40;
0, 18, 32, 42, 48, 50;

Prog

MATLAB code in http://www.cs.ucl.ac.uk/staff/W.Langdon/ftp/misc/A176296.tar

Crossrefs

Sequence in context: A245075 A046666 A276093 * A349232 A194795 A131575

Adjacent sequences: A176293 A176294 A176295 * A176297 A176298 A176299

Keyword

nonn,tabf,more

Author

W. B. Langdon, Dec 07 2010

Status

approved