A133188 Natural numbers listed in three columns: if A004526(n-1) = 0 then row n lists A004526(n-1), A004526(n), 1, otherwise row n lists 1, A004526(n), A004526(n-1).

0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 3, 2, 1, 3, 3, 1, 4, 3, 1, 4, 4, 1, 5, 4, 1, 5, 5, 1, 6, 5, 1, 6, 6, 1, 7, 6, 1, 7, 7, 1, 8, 7, 1, 8, 8, 1, 9, 8, 1, 9, 9, 1, 10, 9, 1, 10, 10, 1, 11, 10, 1, 11, 11, 1, 12, 11, 1, 12, 12, 1, 13, 12, 1, 13, 13, 1, 14, 13, 1, 14, 14, 1, 15, 14, 1, 15, 15

Offset: 1

Author

Paul Curtz, Oct 08 2007

Keywords

• nonn
• easy

Comments

The sum of row n is equal to n. See A004526 (integers repeated), which is the main entry for this sequence. - Omar E. Pol, Mar 19 2008

As a flat sequence, a(n+1) is the number of free trees of n vertices which have the maximum possible terminal Wiener index for n vertices (A349704). [Gutman, Furtula, Petrović, theorem 5] - Kevin Ryde, Nov 27 2021

Examples

			Rows begin:
  n=1:  0, 0, 1;
  n=2:  0, 1, 1;
  n=3:  1, 1, 1;
  n=4:  1, 2, 1;
  n=5:  1, 2, 2;
  n=6:  1, 3, 2;
        ...
		

Links

• Ivan Gutman, Boris Furtula and Miroslav Petrović, Terminal Wiener Index, Journal of Mathematical Chemistry, volume 46, 2009, pages 522-531.

Crossrefs

Cf. A004526, A349704 (maximum terminal Wiener).

Extensions

Edited by Omar E. Pol, Mar 19 2008