A352460 - OEIS

A352460

Triangle read by rows: T(n,k), 2 <= k < n is the number of n-element k-ary unlabeled rooted trees where a subtree consisting of h + 1 nodes has exactly min{h,k} subtrees.

%I #31 May 30 2022 19:36:36

%S 1,1,1,2,1,1,2,2,1,1,4,3,2,1,1,5,4,3,2,1,1,9,6,5,3,2,1,1,13,10,6,5,3,

%T 2,1,1,23,15,10,7,5,3,2,1,1,35,24,14,10,7,5,3,2,1,1,61,39,23,14,11,7,

%U 5,3,2,1,1,98,63,34,21,14,11,7,5,3,2,1,1

%N Triangle read by rows: T(n,k), 2 <= k < n is the number of n-element k-ary unlabeled rooted trees where a subtree consisting of h + 1 nodes has exactly min{h,k} subtrees.

%e Triangle begins:

%e 1;

%e 1, 1;

%e 2, 1, 1;

%e 2, 2, 1, 1;

%e 4, 3, 2, 1, 1;

%e 5, 4, 3, 2, 1, 1;

%e 9, 6, 5, 3, 2, 1, 1;

%e 13, 10, 6, 5, 3, 2, 1, 1;

%e 23, 15, 10, 7, 5, 3, 2, 1, 1;

%e 35, 24, 14, 10, 7, 5, 3, 2, 1, 1;

%e 61, 39, 23, 14, 11, 7, 5, 3, 2, 1, 1;

%e 98, 63, 34, 21, 14, 11, 7, 5, 3, 2, 1, 1;

%e In particular, the rooted trees counted in the first three rows of the triangle are shown by using the Hasse diagram as follows:

%e ---------

%e o o

%e \ /

%e o

%e ----------------------

%e o |

%e | |

%e o o | o o o

%e \ / | \ | /

%e o | o

%e ------------------------------------------------------

%e o o o o | o |

%e \ / | | | | |

%e o o o o | o o o | o o o o

%e \ / \ / | \ | / | \ \ / /

%e o o | o | o

%Y Cf. A000081, A000598, A001190, A292556, A299038.

%K nonn,tabl

%O 3,4

%A _Salah Uddin Mohammad_, Mar 17 2022