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A219671
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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.
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3
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0, 1, 16, 243, 4704, 90930, 1883760, 39868955, 867923840, 19226700486, 432776971200, 9863289713046, 227212909995456, 5281459355486028, 123725917334379360, 2918138849807324715, 69236356202861088384, 1651381196044566423294, 39572852284708565895072
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OFFSET
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0,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..100
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FORMULA
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a(n) ~ c * 26^n / n^(3/2), where c = 0.1102253437... . - Vaclav Kotesovec, Sep 07 2014
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MAPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A219670.
Sequence in context: A207995 A008788 A360759 * A138460 A182148 A304170
Adjacent sequences: A219668 A219669 A219670 * A219672 A219673 A219674
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KEYWORD
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nonn
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AUTHOR
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Jon Perry, Nov 24 2012
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EXTENSIONS
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More terms from Alois P. Heinz, Nov 28 2012
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STATUS
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approved
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