A176296 - OEIS

%I #25 Dec 18 2017 11:36:33

%S 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,

%T 40,0,18,32,42,48,50

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

%C 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.

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

%H W. B. Langdon, <a href="http://dx.doi.org/10.1145/1967654.1967658">Elementary bit string mutation landscapes</a>, Foundations of Genetic Algorithms XI, Proceedings, pp. 25-42.

%e 0, 2;

%e 0, 4;

%e 0, 6, 8;

%e 0, 8, 12;

%e 0, 10, 16, 18;

%e 0, 12, 20, 24;

%e 0, 14, 24, 30, 32;

%e 0, 16, 28, 36, 40;

%e 0, 18, 32, 42, 48, 50;

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

%K nonn,tabf,more

%O 1,2

%A _W. B. Langdon_, Dec 07 2010