cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Jeremy Lovejoy, Sep 29 2022

Keywords

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.

Examples

			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.

Formula

G.f.: (Product_{k>=1}(1+q^k))*Sum_{n>=1}q^(n*(n+1)/2)/Product_{k=1..n}(1+q^k).
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