cp's OEIS Frontend

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).

%I A133188 #9 Nov 28 2021 02:41:21
%S A133188 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,
%T A133188 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,
%U A133188 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
%N 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).
%C A133188 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
%C A133188 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
%H A133188 Ivan Gutman, Boris Furtula and Miroslav Petrović, <a href="https://doi.org/10.1007/s10910-008-9476-2">Terminal Wiener Index</a>, Journal of Mathematical Chemistry, volume 46, 2009, pages 522-531.
%e A133188 Rows begin:
%e A133188   n=1:  0, 0, 1;
%e A133188   n=2:  0, 1, 1;
%e A133188   n=3:  1, 1, 1;
%e A133188   n=4:  1, 2, 1;
%e A133188   n=5:  1, 2, 2;
%e A133188   n=6:  1, 3, 2;
%e A133188         ...
%Y A133188 Cf. A004526, A349704 (maximum terminal Wiener).
%K A133188 nonn,easy
%O A133188 1,11
%A A133188 _Paul Curtz_, Oct 08 2007
%E A133188 Edited by _Omar E. Pol_, Mar 19 2008