A396904 a(n) = number of total diagonals in Johnson solid J_n.

2, 5, 21, 46, 80, 155, 9, 20, 35, 16, 30, 1, 6, 13, 25, 41, 21, 78, 154, 255, 380, 72, 146, 245, 370, 14, 42, 88, 88, 150, 150, 250, 250, 375, 117, 117, 228, 375, 375, 525, 525, 700, 700, 111, 220, 365, 515, 690, 8, 11, 15, 36, 43, 56, 65, 65, 75, 175, 191, 191, 208, 25

Offset

1,1

Comments

The total number of diagonals is the number of space diagonals plus the number of diagonals in all faces.

Links

Paolo Xausa, Table of n, a(n) for n = 1..92 (the full sequence).

Wikipedia, List of Johnson solids.

Formula

a(n) = A396905(n) + A396906(n).

a(n) = binomial(A242733(n),2) - A242732(n).

Example

a(6) = 90 + 65 = 155 because Johnson solid J_6 (pentagonal rotunda) has 90 space diagonals and 65 face diagonals (see A396906 Example).

Mathematica

Binomial[#, 2] - #2 & @@@ Array[PolyhedronData[{"Johnson", #}, {"VertexCount", "EdgeCount"}] &, 92]

Crossrefs

Cf. A242732, A242733, A396905, A396906.

Sequence in context: A328689 A039777 A246167 * A359725 A000941 A000131

Adjacent sequences: A396901 A396902 A396903 * A396905 A396906 A396907

Keyword

nonn,fini,full

Author

Paolo Xausa, Jun 09 2026

Status

approved