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A219671 Number of n-step paths on cubic lattice from (0,0,0) to (1,0,0) with moves in any direction but no zero moves allowed.

%I A219671 #21 Dec 20 2020 03:53:40
%S A219671 0,1,16,243,4704,90930,1883760,39868955,867923840,19226700486,
%T A219671 432776971200,9863289713046,227212909995456,5281459355486028,
%U A219671 123725917334379360,2918138849807324715,69236356202861088384,1651381196044566423294,39572852284708565895072
%N A219671 Number of n-step paths on cubic lattice from (0,0,0) to (1,0,0) with moves in any direction but no zero moves allowed.
%H A219671 Alois P. Heinz, <a href="/A219671/b219671.txt">Table of n, a(n) for n = 0..100</a>
%F A219671 a(n) ~ c * 26^n / n^(3/2), where c = 0.1102253437... . - _Vaclav Kotesovec_, Sep 07 2014
%p A219671 b:= proc(n,p) option remember; `if`(p[3]>n, 0, `if`(n=0, 1,
%p A219671       add(add(add(`if`(i=0 and j=0 and k=0, 0, b(n-1, sort(map(abs,
%p A219671       p+[i, j, k])))), i=-1..1), j=-1..1), k=-1..1)))
%p A219671     end:
%p A219671 a:= n-> b(n, [0$2, 1]):
%p A219671 seq (a(n), n=0..25);  # _Alois P. Heinz_, Nov 28 2012
%t A219671 b[n_, p_] := b[n, p] = If[p[[3]]>n, 0, If[n==0, 1, Sum[Sum[Sum[If[i==0 && j==0 && k==0, 0, b[n-1, Sort[Map[Abs, p + {i, j, k}]]]], {i, -1, 1}], {j, -1, 1}], {k, -1, 1}]]];
%t A219671 a[n_] := b[n, {0, 0, 1}];
%t A219671 a /@ Range[0, 25] (* _Jean-François Alcover_, Dec 20 2020, after _Alois P. Heinz_ *)
%Y A219671 Cf. A219670.
%K A219671 nonn
%O A219671 0,3
%A A219671 _Jon Perry_, Nov 24 2012
%E A219671 More terms from _Alois P. Heinz_, Nov 28 2012