cp's OEIS Frontend

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.

A300695 Irregular triangle read by rows: T(n, k) = number of vertices with rank k in cocoon concertina n-cube.

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%I A300695 #18 Apr 03 2018 10:43:47
%S A300695 1,1,1,1,3,3,1,1,6,13,6,13,6,1
%N A300695 Irregular triangle read by rows: T(n, k) = number of vertices with rank k in cocoon concertina n-cube.
%C A300695 Although the cocoon concertina n-cube has no ranks for n>2, its inner vertices can be forced on the rank layers of the convex solid.
%C A300695 Sum of row n is the number of vertices of a cocoon concertina n-cube, i.e., A000696(n).
%C A300695 The rows are palindromic. Their lengths are the central polygonal numbers A000124 = 1, 2, 4, 7, 11, 16, 22, ... That means after row 0 rows of even and odd length follow each other in pairs.
%C A300695 A300699 is a triangle of the same shape that shows the number of ranks in convex concertina hypercubes.
%H A300695 Tilman Piesk, ranks <a href="https://commons.wikimedia.org/wiki/File:Cocoon_concertina_cube;_ranks_1_and_5.png">1 / 5</a>, <a href="https://commons.wikimedia.org/wiki/File:Cocoon_concertina_cube;_ranks_2_and_4.png">2 / 4</a> and <a href="https://commons.wikimedia.org/wiki/File:Cocoon_concertina_cube;_rank_3.png">3</a> for n=3
%H A300695 Tilman Piesk, <a href="https://github.com/watchduck/concertina_hypercubes/blob/master/cocoon.py">Python code used to generate the sequence</a> (currently unfinished, does not find all ranks for n>3)
%e A300695 First rows of the triangle:
%e A300695     k   0    1    2    3    4    5    6
%e A300695   n
%e A300695   0     1
%e A300695   1     1    1
%e A300695   2     1    3    3    1
%e A300695   3     1    6   13    6   13    6    1
%Y A300695 Cf. A000696, A300699, A000124.
%K A300695 nonn,tabf,more
%O A300695 0,5
%A A300695 _Tilman Piesk_, Mar 13 2018