A135443 Number of maximal directed trails in the labeled n-ladder graph P_2 X P_n.

2, 8, 12, 40, 84, 144, 220, 312, 420, 544, 684, 840, 1012, 1200, 1404, 1624, 1860, 2112, 2380, 2664, 2964, 3280, 3612, 3960, 4324, 4704, 5100, 5512, 5940, 6384, 6844, 7320, 7812, 8320, 8844, 9384, 9940, 10512, 11100, 11704, 12324, 12960, 13612, 14280

Offset

1,1

Links

Table of n, a(n) for n=1..44.

Formula

For n > 2, a(n) = 4 * (n-2) * (2*n - 3) = A033586(n-2). - Max Alekseyev, May 04 2023

Example

For n = 4 the graph is
  .__.__.__.
  |__|__|__|
Names of nodes:
  1 2 3 4
  a b c d
Maximal directed paths which start from node 3:
  34dcba123c
  34dc32ba12
  34dc321ab2
  34dc321abc
  3cd432ba12
  3cd4321ab2
  3cd4321abc
  3cba1234dc
  321abc34dc
  321abcd43c
There are also paths from nodes c,b,2. So n(4) = 4*10 = 40.

Crossrefs

Apart from initial terms sequence is the same as A033586.

Cf. A003682, A089243.

Sequence in context: A285551 A143231 A104039 * A280092 A083546 A013190

Adjacent sequences: A135440 A135441 A135442 * A135444 A135445 A135446

Keyword

nonn,walk

Author

Yasutoshi Kohmoto, Feb 18 2008

Extensions

Edited and extended by Max Alekseyev, May 04 2023

Status

approved