login
Number of double nodes (exactly two nodes on that level) for all Motzkin paths of length n.
3

%I #15 Apr 16 2024 18:01:36

%S 0,1,1,2,6,14,32,74,180,457,1195,3177,8526,23018,62441,170153,465791,

%T 1280956,3538618,9817619,27348480,76467497,214532805,603732396,

%U 1703728554,4819990947,13667248631,38834528740,110556072877,315290709729,900635841754,2576615923655,7381956798465,21177682172332,60832837964492

%N Number of double nodes (exactly two nodes on that level) for all Motzkin paths of length n.

%e Of the 9 Motzkin paths of length 4 the following 5 have a total of 6 double nodes:

%e |1......|

%e |2../\..|3..__..|2.._...|2..._..|2......|

%e |2./..\.|2./..\.|3./.\_.|3._/.\.|3./\/\.|

%Y Cf. A001006, A088457.

%Y Column k=2 of A372014.

%K nonn

%O 0,4

%A _Wenjin Woan_

%E Edited by _Michael Somos_, Sep 29, 2003

%E a(16)-a(34) from _Alois P. Heinz_, Apr 13 2024