A352880 Triangle read by rows: T(n,k) = number of vertices of degree k in an origami flip graph OFG(A2n).

8, 12, 18, 16, 64, 32, 20, 150, 200, 50, 24, 288, 720, 480, 72, 28, 490, 1960, 2450, 980, 98, 32, 768, 4480, 8960, 6720, 1792, 128, 36, 1134, 9072, 26460, 31752, 15876, 3024, 162, 40, 1600, 16800, 67200, 117600, 94080, 33600, 4800, 200, 44, 2178, 29040, 152460, 365904, 426888, 243936, 65340, 7260, 242

Offset

2,1

Comments

See page 2 of Hull, et al. (2022) for a description of OFG(A_2n).

Links

Michael De Vlieger, Table of n, a(n) for n = 2..11176 (rows 2..150, flattened)

Thomas C. Hull, Manuel Morales, Sarah Nash, and Natalya Ter-Saakov, Maximal origami flip graphs of flat-foldable vertices: properties and algorithms, arXiv:2203.14173 [math.CO], 2022, p. 13.

Formula

T(n,k) = (4n/(n+1)) * binomial(n+1, k-n-1) * binomial(n-2, k-n-2) for n+2 <= k <= 2n.

Example

Table begins:
  2n\k |  4   5   6   7    8    9   10   11  12
  ---------------------------------------------
    4  |  8
    6  |     12  18
    8  |         16  64   32
   10  |             20  150  200   50
   12  |                  24  288  720  480  72
   ...

Mathematica

Table[(4 n/(n + 1)) Binomial[n + 1, k - n - 1] Binomial[n - 2, k - n - 2], {n, 2, 11}, {k, n + 2, 2 n}] // Flatten

Crossrefs

Sequence in context: A030752 A091523 A257162 * A104201 A036327 A340681

Adjacent sequences: A352877 A352878 A352879 * A352881 A352882 A352883

Keyword

nonn,tabl,easy

Author

Michael De Vlieger, Apr 06 2022

Status

approved