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A357320
The total number of fixed points among all strict partitions of n, when parts are written in increasing order.
0
0, 1, 0, 2, 1, 1, 4, 3, 4, 4, 9, 8, 11, 12, 15, 21, 24, 28, 34, 40, 46, 60, 67, 80, 93, 110, 125, 148, 174, 200, 231, 268, 306, 354, 404, 461, 534, 606, 690, 786, 895, 1012, 1150, 1298, 1467, 1662, 1872, 2104, 2374, 2664, 2990, 3355, 3759, 4202, 4702, 5256
OFFSET
0,4
COMMENTS
For instance, the partition (1,2,4,7,11) = (y(1),y(2),y(3),y(4),y(5)) has 2 fixed points, since y(1) = 1 and y(2) = 2.
FORMULA
G.f.: (Product_{k>=1}(1+q^k))*Sum_{n>=1}q^(n*(n+1)/2)/Product_{k=1..n}(1+q^k).
EXAMPLE
The 10 strict partition of 10 are (1,2,3,4), (2,3,5), (1,4,5), (1,3,6), (4,6), (1,2,7), (3,7), (2,8), (1,9), and (10), containing 4,0,1,1,0,2,0,0,1, and 0 fixed points, respectively, and so a(10) = 9.
CROSSREFS
For the same count but where parts are written in decreasing order, see A352829.
For the case of ordinary partitions, see A357459.
Sequence in context: A078015 A366781 A240769 * A174455 A245596 A326611
KEYWORD
nonn
AUTHOR
Jeremy Lovejoy, Sep 29 2022
STATUS
approved