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 A348149 #25 Jun 06 2023 03:09:00 %S A348149 4,9,14,20,26,33,40,48,55,64 %N 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. %C A348149 In this variation of A347581 the areas must be added in the order of their sizes, from 1 through n, and as each area is added the minimum possible number of line segments must be used. This forces, for example, the first three areas of size 1, 2 and 3 to form a 2 X 3 block and thus they can never appear in any other arrangement in the final area. This is also true for n up to at least 9 due to the restriction of maximizing the usable edges for the next area. This leads to a(8) and a(10) containing one more line segment than the optimal solutions of A347581. %H A348149 Sascha Kurz, <a href="https://arxiv.org/abs/math/0506428">Counting polyominoes with minimum perimeter</a>, arXiv:math/0506428 [math.CO], 2015. %e A348149 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. %e A348149 . %e A348149 __ %e A348149 |__| a(1) = 4 %e A348149 __ __ __ %e A348149 |__|__ __| a(2) = 9 %e A348149 __ __ __ %e A348149 |__|__ __| a(3) = 14 %e A348149 |__ __ __| %e A348149 __ __ __ %e A348149 |__|__ __| %e A348149 |__ __ __| a(4) = 20 %e A348149 | | %e A348149 |__ __| %e A348149 __ __ __ %e A348149 |__|__ __|__ %e A348149 |__ __ __| | a(5) = 26 %e A348149 | | | %e A348149 |__ __|__ __| %e A348149 __ __ __ %e A348149 |__|__ __|__ __ __ %e A348149 |__ __ __| | | a(6) = 33 %e A348149 | | | | %e A348149 |__ __|__ __|__ __| %e A348149 __ __ __ __ %e A348149 __ __|__ | %e A348149 |__|__ __|__ __ __| %e A348149 |__ __ __| | | a(7) = 40 %e A348149 | | | | %e A348149 |__ __|__ __|__ __| %e A348149 __ __ __ __ %e A348149 | | %e A348149 |__ __ __ __| %e A348149 __ __|__ | %e A348149 |__|__ __|__ __ __| a(8) = 48 %e A348149 |__ __ __| | | %e A348149 | | | | %e A348149 |__ __|__ __|__ __| %e A348149 __ __ __ __ __ __ __ %e A348149 | | | %e A348149 | |__ __ __ __| %e A348149 |__ __ __|__ | %e A348149 |__|__ __|__ __ __| a(9) = 55 %e A348149 |__ __ __| | | %e A348149 | | | | %e A348149 |__ __|__ __|__ __| %e A348149 __ __ __ __ __ __ __ %e A348149 | | | %e A348149 | |__ __ __ __| %e A348149 __|__ __ __|__ | %e A348149 | |__|__ __|__ __ __| a(10) = 64 %e A348149 | |__ __ __| | | %e A348149 | | | | | %e A348149 | |__ __|__ __|__ __| %e A348149 |__ __| %e A348149 . %Y A348149 Cf. A347581, A001168, A291808, A291809, A328020, A291806, A006983. %K A348149 nonn,more %O A348149 1,1 %A A348149 _Scott R. Shannon_, Oct 03 2021