Pascal's triangle: Difference between revisions

<lang Mathematica>n=7;

Column[StringReplace[ToString /@ Replace[MatrixExp[SparseArray[

A more graphical output with arrows would involve the plotting functionality with Graph[]:

<lang Mathematica>nmax := 10;

pascal[nmax_] := Module[

{vals = Table[Binomial[n, k], {n, 0, nmax}, {k, 0, n}],

ids = Table[{n, k}, {n, 0, nmax}, {k, 0, n}],

labels, left, right, leftright, edgeLabels

},

labels = Flatten[Thread /@ (Thread[ids -> vals]), 1];

left = DeleteCases[Flatten[Flatten[ids, 1] /. {n_, k_} /; (n >= k + 1) :> {{n, k + 1} -> {n + 1, k + 1}}, 1], _?NumberQ];

right = DeleteCases[Flatten[Flatten[ids, 1] /. {n_, k_} /; (n > k) :> {{n, k} -> {n + 1, k + 1}}, 1], _?NumberQ];

leftright = DeleteCases[left \[Union] right, _ -> {b_, _} /; b > nmax];

edgeLabels = (# -> Style["+", Medium] & /@ leftright);

Graph[Flatten[ids, 1], leftright

, VertexLabels -> MapAt[Placed[#, Center] &, labels, {All, 2}]

, GraphLayout -> "SpringEmbedding"

, VertexSize -> 0.8, EdgeLabels -> edgeLabels

, PlotLabel -> "Pascal's Triangle"

]

];

pascal[nmax]

</lang>