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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. 3
 0, 1, 16, 243, 4704, 90930, 1883760, 39868955, 867923840, 19226700486, 432776971200, 9863289713046, 227212909995456, 5281459355486028, 123725917334379360, 2918138849807324715, 69236356202861088384, 1651381196044566423294, 39572852284708565895072 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..100 FORMULA a(n) ~ c * 26^n / n^(3/2), where c = 0.1102253437... . - Vaclav Kotesovec, Sep 07 2014 MAPLE b:= proc(n, p) option remember; `if`(p[3]>n, 0, `if`(n=0, 1, add(add(add(`if`(i=0 and j=0 and k=0, 0, b(n-1, sort(map(abs, p+[i, j, k])))), i=-1..1), j=-1..1), k=-1..1))) end: a:= n-> b(n, [0\$2, 1]): seq (a(n), n=0..25); # Alois P. Heinz, Nov 28 2012 MATHEMATICA 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}]]]; a[n_] := b[n, {0, 0, 1}]; a /@ Range[0, 25] (* Jean-François Alcover, Dec 20 2020, after Alois P. Heinz *) CROSSREFS Cf. A219670. Sequence in context: A207995 A008788 A360759 * A138460 A182148 A304170 Adjacent sequences: A219668 A219669 A219670 * A219672 A219673 A219674 KEYWORD nonn AUTHOR Jon Perry, Nov 24 2012 EXTENSIONS More terms from Alois P. Heinz, Nov 28 2012 STATUS approved

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Last modified March 29 01:21 EDT 2023. Contains 361596 sequences. (Running on oeis4.)