A135443 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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 a(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