A348149 Variation of the Barnyard sequence A347581: a(n) is the minimum number of unit-length line segments required to enclose areas of 1 through n on a square grid when the number of segments is minimized as each area of incrementing size, starting at 1, is added.
4, 9, 14, 20, 26, 33, 40, 48, 55, 64
Offset: 1
Examples
Examples of n = 1 to n = 10 are given below. Note that for a(3) the configuration could also consist of the area of size 1 sitting above the area of size 2 with the area of size 3 forming an L-shaped block creating the minimal 2 X 3 block.
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|__| a(1) = 4
__ __ __
|__|__ __| a(2) = 9
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|__|__ __| a(3) = 14
|__ __ __|
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|__|__ __|
|__ __ __| a(4) = 20
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|__|__ __|__
|__ __ __| | a(5) = 26
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|__ __|__ __|
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|__|__ __|__ __ __
|__ __ __| | | a(6) = 33
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|__ __|__ __|__ __|
__ __ __ __
__ __|__ |
|__|__ __|__ __ __|
|__ __ __| | | a(7) = 40
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|__ __|__ __|__ __|
__ __ __ __
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|__ __ __ __|
__ __|__ |
|__|__ __|__ __ __| a(8) = 48
|__ __ __| | |
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|__ __|__ __|__ __|
__ __ __ __ __ __ __
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| |__ __ __ __|
|__ __ __|__ |
|__|__ __|__ __ __| a(9) = 55
|__ __ __| | |
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|__ __|__ __|__ __|
__ __ __ __ __ __ __
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| |__ __ __ __|
__|__ __ __|__ |
| |__|__ __|__ __ __| a(10) = 64
| |__ __ __| | |
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Links
- Sascha Kurz, Counting polyominoes with minimum perimeter, arXiv:math/0506428 [math.CO], 2015.
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