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%I #3 Mar 31 2012 12:35:48
%S 1,1,2,1,3,5,1,4,12,13,1,5,22,51,35,1,6,35,130,226,96,1,7,51,265,803,
%T 1025,267,1,8,70,471,2100,5085,4724,750,1,9,92,763,4556,17075,32747,
%U 22022,2123,1,10,117,1156,8715,45241,141246,213419,103550,6046,1,11,145
%N T(n,k)=number of sequences of n integers p(i) i=0..n-1 0<=p(i)<=k*i and |p(i+1)-p(i)|<=k
%C Paths down a n-high rectangular-grid right triangle with interior neighbor fanout 2*k+1
%C Table starts
%C ....1......1.......1........1.........1..........1..........1...........1
%C ....2......3.......4........5.........6..........7..........8...........9
%C ....5.....12......22.......35........51.........70.........92.........117
%C ...13.....51.....130......265.......471........763.......1156........1665
%C ...35....226.....803.....2100......4556.......8715......15226.......24843
%C ...96...1025....5085....17075.....45241.....102221.....205990......380805
%C ..267...4724...32747...141246....457147....1220268....2836590.....5941923
%C ..750..22022..213419..1182719...4676643...14749175...39552570....93886185
%C .2123.103550.1403399..9994086..48284749..179930563..556668807..1497389568
%C .6046.490191.9292850.85049639.502090660.2210840169.7891281877.24055051863
%H R. H. Hardin, <a href="/A180906/b180906.txt">Table of n, a(n) for n=1..9999</a>
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_ Sep 23 2010
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