OFFSET
1,11
FORMULA
If k divides n, T(n,k) = A078374(n/k); otherwise T(n,k) = 0.
EXAMPLE
Triangle begins:
01: 1
02: 0 1
03: 1 0 1
04: 1 0 0 1
05: 2 0 0 0 1
06: 2 1 0 0 0 1
07: 4 0 0 0 0 0 1
08: 4 1 0 0 0 0 0 1
09: 6 0 1 0 0 0 0 0 1
10: 7 2 0 0 0 0 0 0 0 1
11: 11 0 0 0 0 0 0 0 0 0 1
12: 10 2 1 1 0 0 0 0 0 0 0 1
13: 17 0 0 0 0 0 0 0 0 0 0 0 1
14: 17 4 0 0 0 0 0 0 0 0 0 0 0 1
15: 23 0 2 0 1 0 0 0 0 0 0 0 0 0 1
The strict partitions counted in row 12 are the following.
T(12,1) = 10: (11,1) (9,2,1) (8,3,1) (7,5) (7,4,1) (7,3,2) (6,5,1) (6,3,2,1) (5,4,3) (5,4,2,1)
T(12,2) = 2: (10,2) (6,4,2)
T(12,3) = 1: (9,3)
T(12,4) = 1: (8,4)
T(12,12) = 1: (12)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&GCD@@#===k&]], {n, 15}, {k, n}]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Apr 19 2018
STATUS
approved