A239688 Number of paths joining opposite corners of an n X 2 grid with every vertex appearing at most twice in the path.

2, 22, 218, 2100, 20701, 202664, 1990006, 19519656, 191538146, 1879225062, 18438413081, 180909222618, 1775009067937, 17415641736474, 170875080099492, 1676555203866592, 16449663882025188, 161397269556516646, 1583562991844385082, 15537262462108603226

Offset

1,1

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 100 terms from Muhammad Kholilurrohman)

Formula

G.f.: -(8*x^10 +17*x^9 -38*x^8 -60*x^7 +74*x^6 +55*x^5 -56*x^4 -10*x^3 +6*x^2 +2*x) / (4*x^12 -20*x^11 -71*x^10 +116*x^9 +197*x^8 -268*x^7 -129*x^6 +252*x^5 -31*x^4 -80*x^3 +26*x^2 +8*x -1). - Alois P. Heinz, Nov 16 2014

Example

The 22 paths in a 2 X 2 grid whose nodes are numbered from 1 to 4 in the natural way are 124, 134, 12124, 12134, 12424, 12434, 13124, 13134, 13424, 13434, 1212434, 1213424, 1213434, 1242134, 1243124, 1243134, 1312424, 1312434, 1313424, 1342124, 1342134, 1343124.

Crossrefs

Sequence in context: A366919 A308313 A304024 * A350965 A336894 A037567

Adjacent sequences: A239685 A239686 A239687 * A239689 A239690 A239691

Keyword

nonn

Author

Giovanni Resta, Mar 24 2014

Extensions

a(21)-a(40) from Muhammad Kholilurrohman, Nov 16 2014

Status

approved