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.
%I A347581 #56 Oct 06 2021 12:17:35 %S A347581 4,9,14,20,26,33,40,47,55,63 %N A347581 The Barnyard sequence: a(n) is the minimum number of unit length line segments required to enclose areas of 1 through n on a square grid. %C A347581 The areas of size 1 through n can be created in any order and position, the only requirement being the final number of line segments used to enclose all areas is minimized. It is likely the perimeter of each area of size k, 1 <= k <= n, is the minimum possible for an area of size k, although this is unknown. %C A347581 See A348149 for the total segments when the number of segments at each step is minimized. %H A347581 Sascha Kurz, <a href="https://arxiv.org/abs/math/0506428">Counting polyominoes with minimum perimeter</a>, arXiv:math/0506428 [math.CO], 2015. %e A347581 Example areas using the minimum number of line segments from n = 1 through n = 10 are: %e A347581 . %e A347581 __ %e A347581 |__| a(1) = 4 %e A347581 __ __ __ %e A347581 |__|__ __| a(2) = 9 %e A347581 __ __ __ %e A347581 |__|__ __| a(3) = 14 %e A347581 |__ __ __| %e A347581 __ __ __ %e A347581 |__|__ __| %e A347581 |__ __ __| a(4) = 20 %e A347581 | | %e A347581 |__ __| %e A347581 __ __ __ %e A347581 |__|__ __|__ %e A347581 |__ __ __| | a(5) = 26 %e A347581 | | | %e A347581 |__ __|__ __| %e A347581 __ __ __ %e A347581 |__|__ __|__ __ __ %e A347581 |__ __ __| | | a(6) = 33 %e A347581 | | | | %e A347581 |__ __|__ __|__ __| %e A347581 __ __ __ __ %e A347581 __ __|__ | %e A347581 |__|__ __|__ __ __| %e A347581 |__ __ __| | | a(7) = 40 %e A347581 | | | | %e A347581 |__ __|__ __|__ __| %e A347581 __ __ __ __ __ __ %e A347581 | | | %e A347581 |__ __ __ __| | %e A347581 | |__ __ __| a(8) = 47 %e A347581 |__ __ __|__ | %e A347581 | | | |__ __| %e A347581 |__ __|__|__ __|__| %e A347581 __ __ __ __ __ __ __ %e A347581 | | | %e A347581 | |__ __ __ __| %e A347581 |__ __ __|__ | %e A347581 |__|__ __|__ __ __| a(9) = 55 %e A347581 |__ __ __| | | %e A347581 | | | | %e A347581 |__ __|__ __|__ __| %e A347581 __ __ __ __ __ __ __ __ %e A347581 | __|__ | | %e A347581 |__ __ __| |__|__ | %e A347581 | | | |__| %e A347581 | | | | | a(10) = 63 %e A347581 |__ __ __|__ __|__ __|__| %e A347581 | | |__| %e A347581 |__ __ __ __ __|__ __| %e A347581 . %Y A347581 Cf. A348149, A001168, A291808, A291809, A328020, A291806, A172477, A006983. %K A347581 nonn,more %O A347581 1,1 %A A347581 _Scott R. Shannon_, Oct 05 2021