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%I #28 Oct 27 2023 22:12:52
%S 2,22,218,2100,20701,202664,1990006,19519656,191538146,1879225062,
%T 18438413081,180909222618,1775009067937,17415641736474,
%U 170875080099492,1676555203866592,16449663882025188,161397269556516646,1583562991844385082,15537262462108603226
%N Number of paths joining opposite corners of an n X 2 grid with every vertex appearing at most twice in the path.
%H Alois P. Heinz, <a href="/A239688/b239688.txt">Table of n, a(n) for n = 1..1000</a> (first 100 terms from Muhammad Kholilurrohman)
%F 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
%e 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.
%K nonn
%O 1,1
%A _Giovanni Resta_, Mar 24 2014
%E a(21)-a(40) from _Muhammad Kholilurrohman_, Nov 16 2014
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