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

Author

Giovanni Resta, Mar 24 2014

Keywords

• nonn

Examples

			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.
		

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

Extensions

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