A219986 Number of n-step paths on a quartic lattice that move from (0,0,0,0) to (1,0,0,1) allowing all moves in {-1,0,1}^4 inclusive the zero move.

0, 1, 36, 1764, 92416, 5267025, 315630756, 19684370601, 1264977082944, 83266957255329, 5588691282002500, 381203015928291216, 26357375491548319296, 1843677173726039815969, 130261796682232750056900, 9284172482167489217304900, 666818520819487582805692416

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..60

Maple

b:= proc(n, p) option remember; `if`(p[4]>n, 0, `if`(n=0, 1,
      add(add(add(add(b(n-1, sort(map(abs, p+[i, j, k, m])))
      , i=-1..1), j=-1..1), k=-1..1), m=-1..1)))
    end:
a:= n-> b(n, [0$2, 1$2]):
seq(a(n), n=0..20);  # Alois P. Heinz, Dec 02 2012

Mathematica

b[n_, p_] := b[n, p] = If[p[[4]] > n, 0, If[n == 0, 1,
     Sum[Sum[Sum[Sum[b[n-1, Sort[Abs[ p + {i, j, k, m}]]],
     {i, -1, 1}], {j, -1, 1}], {k, -1, 1}], {m, -1, 1}]]];
a[n_] := b[n, {0, 0, 1, 1}];
Table [a[n], {n, 0, 20}] (* Jean-François Alcover, Apr 28 2022, after Alois P. Heinz *)

Prog

(JavaScript)
b=new Array();
for (i1=-1; i1<2; i1++)
for (i2=-1; i2<2; i2++)
for (i3=-1; i3<2; i3++)
for (i4=-1; i4<2; i4++) {
n=(i1+1)+(i2+1)*3+(i3+1)*9+(i4+1)*27;
b[n]=[i1, i2, i3, i4];
}
function inc(arr, m) {
al=arr.length-1;
full=true;
for (ac=0; ac<=al; ac++) if (arr[ac]!=m) {full=false; break; }
if (full==true) return false;
while (arr[al]==m && al>0) {arr[al]=0; al--; }
arr[al]++;
return true;
}
for (k=0; k<5; k++) {
c=0;
a=new Array();
for (i=0; i<k; i++) a[i]=0;
for (i=0; i<Math.pow(81, k); i++) {
p=[0, 0, 0, 0];
for (j=0; j<k; j++) {p[0]+=b[a[j]][0]; p[1]+=b[a[j]][1]; p[2]+=b[a[j]][2]; p[3]+=b[a[j]][3]; }
if (p[0]==1 && p[1]==0 && p[2]==0 && p[3]==1) c++;
inc(a, 80);
}
document.write(c+", ");
}

Crossrefs

Cf. A219670, A219671.

Sequence in context: A270602 A190918 A356730 * A113618 A054980 A151640

Adjacent sequences: A219983 A219984 A219985 * A219987 A219988 A219989

Keyword

nonn

Author

Jon Perry, Dec 02 2012

Extensions

More terms from Alois P. Heinz, Dec 02 2012

Status

approved