

A370386


Irregular triangle read by rows. An infinite rooted tree having root node 1 in row n = 0. Nodes in row n each have n + 1 children with values m + k, where m is the value of the parent node and k takes the values of all nodes from the root to the parent including the parent itself.


1



1, 2, 3, 4, 4, 5, 6, 5, 6, 8, 5, 6, 7, 8, 6, 7, 8, 10, 7, 8, 9, 12, 6, 7, 9, 10, 7, 8, 10, 12, 9, 10, 12, 16, 6, 7, 8, 9, 10, 7, 8, 9, 10, 12, 8, 9, 10, 11, 14, 9, 10, 11, 12, 16, 7, 8, 9, 11, 12, 8, 9, 10, 12, 14, 9, 10, 11, 13, 16, 11, 12, 13, 15, 20, 8, 9
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OFFSET

0,2


COMMENTS

The paths through the tree represent integer partitions which contain their own first differences and have least part 1. These partitions are counted, including those with any least part, in A364673.


LINKS



EXAMPLE

Triangle begins:
1;
2;
3, 4;
4, 5, 6, 5, 6, 8;
5, 6, 7, 8, 6, 7, 8, 10, 7, 8, 9, 12, 6, 7, 9, 10, 7, 8, 10, 12, 9, 10, 12, 16;
...
The tree starts with root 1 in row n = 0. In row n = 2 the parent node 4 has 3 children using values of k: 1, 2, and 4.
Tree begins:
row
[n]
[0] 1

[1] ____2____
/ \
[2] __3__ __4__
/  \ /  \
[3] 4 5 6 5 6 8


PROG

(Python)
A, C = [[(1, )]], [[1]]
for i in range(maxrow):
A.append([])
C.append([])
for j in A[i]:
for k in j:
x = j + (j[1] + k, )
A[i+1].append(x)
C[i+1].append(x[1])
return(C)


CROSSREFS

The tree if only distinct values are allowed is A114622.


KEYWORD

nonn,easy,tabf


AUTHOR



STATUS

approved



