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.
4 example graphs: o
/ \
o o---o
/ \ / \ / \
o o---o o---o---o
/ \ / \ / \ / \ / \ / \
o o---o o---o---o o---o---o---o
n: 1 2 3 4
Vertices: 1 3 6 10
Edges: 0 3 9 18
The 2 X 2 X 2 triangular grid is equal to the cycle graph C_3 with chromatic polynomial q^3 -3*q^2 +2*q => [1, -3, 2, 0].
Triangle T(n,k) begins:
1, 0;
1, -3, 2, 0;
1, -9, 32, -56, 48, -16, 0;
1, -18, 144, -672, 2016, -4031, 5368, ...
1, -30, 419, -3612, 21477, -93207, 304555, ...
1, -45, 965, -13115, 126720, -925528, 5303300, ...
...
4 example graphs: o
/ \
o o---o
/ \ / \ / \
( ) o---o o---o---o
/ \ / \ / \ / \ / \
( ) o---o o---o---o o---o---o---o
n: 1 2 3 4
Vertices: 0 2 6 10
Edges: 0 1 9 18
Matchings: 1 1 2 6
with(LinearAlgebra):
a:= proc(n) option remember; local i, j, h0, h1, M, s, t;
if n<2 then 1
else s:= `if`(member(irem(n, 4), [1, 2]), 1, 0);
M:= Matrix((n+1)*n/2 -s, shape=skewsymmetric);
if s=1 then M[1,2]:=1 fi;
for j from 1+s to n-1 do
h0:= j*(j-1)/2 +1-s;
h1:= h0+j;
t:= 1;
for i from 1 to j do
M[h1, h1+1]:= 1;
M[h1, h0]:= t;
h1:= h1+1;
M[h1, h0]:= t;
h0:= h0+1;
t:= -t
od
od;
sqrt(Determinant(M))
fi
end:
seq(a(n), n=0..15);
a[n_] := a[n] = Module[{i, j, h0, h1, M, s, t}, If[n<2, 1, s = If[1 <= Mod[n, 4] <= 2, 1, 0]; M = Array[0&, {(n+1)n/2 - s, (n+1)n/2 - s}]; If[s == 1, M[[1, 2]] = 1]; For[j = 1+s, j <= n-1, j++, h0 = j(j-1)/2 + 1 - s; h1 = h0+j; t = 1; For[i = 1, i <= j, i++, M[[h1, h1+1]] = 1; M[[h1, h0]] = t; h1 = h1+1; M[[h1, h0]] = t; h0 = h0+1; t = -t]]; Sqrt[Det[M-Transpose[M]]]]];
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Sep 23 2022, after Alois P. Heinz *)
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