A357320 The total number of fixed points among all strict partitions of n, when parts are written in increasing order.

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.

Links

Table of n, a(n) for n=0..55.

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

Adjacent sequences: A357317 A357318 A357319 * A357321 A357322 A357323

Keyword

nonn

Author

Jeremy Lovejoy, Sep 29 2022

Status

approved