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

Author

Jon Perry, Dec 02 2012

Keywords

• nonn

Links

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

Crossrefs

Cf. A219670, A219671.

Programs

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
				

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 *)

Extensions

More terms from Alois P. Heinz, Dec 02 2012