

A352833


Irregular triangle read by rows where T(n,k) is the number of integer partitions of n with k fixed points, k = 0, 1.


17



1, 0, 0, 1, 1, 1, 2, 1, 3, 2, 4, 3, 6, 5, 8, 7, 12, 10, 16, 14, 23, 19, 30, 26, 42, 35, 54, 47, 73, 62, 94, 82, 124, 107, 158, 139, 206, 179, 260, 230, 334, 293, 420, 372, 532, 470, 664, 591, 835, 740, 1034, 924, 1288, 1148, 1588, 1422, 1962, 1756, 2404, 2161
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,7


COMMENTS

A fixed point of a sequence y is an index y(i) = i. A fixed point of a partition is unique if it exists, so all columns k > 1 are zeros.
Conjecture:


LINKS



EXAMPLE

Triangle begins:
0: {1,0}
1: {0,1}
2: {1,1}
3: {2,1}
4: {3,2}
5: {4,3}
6: {6,5}
7: {8,7}
8: {12,10}
9: {16,14}
For example, row n = 7 counts the following partitions:
(7) (52)
(61) (421)
(511) (322)
(43) (3211)
(4111) (2221)
(331) (22111)
(31111) (1111111)
(211111)


MATHEMATICA

pq[y_]:=Length[Select[Range[Length[y]], #==y[[#]]&]];
Table[Length[Select[IntegerPartitions[n], pq[#]==k&]], {n, 0, 15}, {k, 0, 1}]


CROSSREFS

The version counting strong nonexcedances is A114088.
The version for reversed partitions is A238352.


KEYWORD

nonn,tabf


AUTHOR



STATUS

approved



