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A337401 Triangle read by rows: T(n,w) is the number of n-step self avoiding walks on a 3D cubic lattice confined inside a tube of cross section 2w X 2w where the walk starts at the center of the tube's side.

%I A337401 #39 Sep 20 2020 01:16:47
%S A337401 5,19,21,72,91,93,258,383,407,409,926,1638,1821,1851,1853,3176,6856,
%T A337401 8019,8295,8331,8333,11000,28810,35506,37531,37921,37963,37965,36988,
%U A337401 119106,155492,168399,171691,172215,172263,172265,125302,492766,683126,758182,781811,786823,787501,787555,787557
%N A337401 Triangle read by rows: T(n,w) is the number of n-step self avoiding walks on a 3D cubic lattice confined inside a tube of cross section 2w X 2w where the walk starts at the center of the tube's side.
%H A337401 Scott R. Shannon, <a href="/A337401/a337401.txt">Data for n=1 to n=14</a>.
%F A337401 For w>=n, T(n,w) = A116904(n).
%e A337401 T(2,1) = 19 as after a step in one of the two directions toward the adjacent tube side the walk must turn along the side; this eliminates the 2-step straight walk in those two directions, so the total number of walks is 4*4 + 5 - 2 = 19.
%e A337401 The table begins:
%e A337401 5;
%e A337401 19,21;
%e A337401 72,91,93;
%e A337401 258,383,407,409;
%e A337401 926,1638,1821,1851,1853;
%e A337401 3176,6856,8019,8295,8331,8333;
%e A337401 11000,28810,35506,37531,37921,37963,37965;
%e A337401 36988,119106,155492,168399,171691,172215,172263,172265;
%e A337401 125302,492766,683126,758182,781811, 786823,787501,787555,787557;
%e A337401 414518,2013142,2981996,3393526,3545117,3585297,3592551,3593403,3593463,3593465;
%Y A337401 Cf. A337400 (start at middle of tube), A337403 (start at tube's edge), A116904 (w->infinity), A001412, A337023, A259808, A039648.
%K A337401 nonn,walk,tabl
%O A337401 1,1
%A A337401 _Scott R. Shannon_, Aug 26 2020