OFFSET
0,1
COMMENTS
LINKS
Shawn A. Broyles, Table of n, a(n) for n = 0..1000
EXAMPLE
Construction of a minimalist version 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)
A000041(n): 1 2 3 5 7 11 (open regions)
A139582(n): 2 4 6 10 14 22 (line segments)
a(n)......: 3 6 9 15 21 33 (vertices)
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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 ................................................. _ _ _ _ _ _|
.
The r-th horizontal line segment has length A141285(r).
The r-th vertical line segment has length A194446(r).
An infinite diagram is a minimalist table of all partitions of all positive integers.
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Feb 10 2018
STATUS
approved