OFFSET
0,2
COMMENTS
LINKS
Shawn A. Broyles, Table of n, a(n) for n = 0..1000
FORMULA
EXAMPLE
Construction of a modular table of partitions in which a(n) is the number of vertices of the diagram after n-th stage (n = 1..6):
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n ........: 1 2 3 4 5 6 (stage)
a(n)......: 4 7 10 16 22 34 (vertices)
A299474(n): 4 8 12 20 28 44 (edges)
A000041(n): 1 2 3 5 7 11 (regions)
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r p(n)
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. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
1 .... 1 ....|_| |_| | |_| | | |_| | | | |_| | | | | |_| | | | | |
2 .... 2 .........|_ _| |_ _| | |_ _| | | |_ _| | | | |_ _| | | | |
3 .... 3 ................|_ _ _| |_ _ _| | |_ _ _| | | |_ _ _| | | |
4 |_ _| | |_ _| | | |_ _| | | |
5 .... 5 .........................|_ _ _ _| |_ _ _ _| | |_ _ _ _| | |
6 |_ _ _| | |_ _ _| | |
7 .... 7 ....................................|_ _ _ _ _| |_ _ _ _ _| |
8 |_ _| | |
9 |_ _ _ _| |
10 |_ _ _| |
11 .. 11 .................................................|_ _ _ _ _ _|
.
Apart from the axis x, the r-th horizontal line segment has length A141285(r), equaling the largest part of the r-th region of the diagram.
Apart from the axis y, the r-th vertical line segment has length A194446(r), equaling the number of parts in the r-th region of the diagram.
The total number of parts equals the sum of largest parts.
Note that every diagram contains all previous diagrams.
An infinite diagram is a table of all partitions of all positive integers.
PROG
(PARI) a(n) = if (n==0, 1, 1+3*numbpart(n)); \\ Michel Marcus, Jul 15 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Feb 11 2018
STATUS
approved