%I #3 Mar 31 2012 12:35:48

%S 1,1,2,1,3,4,1,4,11,8,1,5,21,42,16,1,6,34,116,163,32,1,7,50,245,659,

%T 639,64,1,8,69,444,1827,3802,2520,128,1,9,91,728,4095,13875,22146,

%U 9976,256,1,10,116,1112,7996,38532,106612,129838,39595,512,1,11,144,1611,14168

%N T(n,k)=number of sequences of n integers p(i) i=0..n-1 0<=p(i)<=k*i and -k<p(i+1)-p(i)<=k

%C Paths down a n-high staggered-grid minimally right-leaning right triangle with interior neighbor fanout 2*k

%C Table starts

%C ...1......1.......1........1.........1..........1..........1...........1

%C ...2......3.......4........5.........6..........7..........8...........9

%C ...4.....11......21.......34........50.........69.........91.........116

%C ...8.....42.....116......245.......444........728.......1112........1611

%C ..16....163.....659.....1827......4095.......7996......14168.......23354

%C ..32....639....3802....13875.....38532......89712.....184564......346392

%C ..64...2520...22146...106612....367322....1020651....2439577.....5215708

%C .128...9976..129838...825764...3533112...11723768...32572164....79355229

%C .256..39595..764731..6432933..34204975..135611317..438101477..1216613579

%C .512.157441.4519504.50331286.332775412.1576988939.5925607074.18760964625

%H R. H. Hardin, <a href="/A180915/b180915.txt">Table of n, a(n) for n=1..9999</a>

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_ Sep 23 2010