A219986 - OEIS

%I #18 Apr 28 2022 05:33:38

%S 0,1,36,1764,92416,5267025,315630756,19684370601,1264977082944,

%T 83266957255329,5588691282002500,381203015928291216,

%U 26357375491548319296,1843677173726039815969,130261796682232750056900,9284172482167489217304900,666818520819487582805692416

%N 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.

%H Alois P. Heinz, <a href="/A219986/b219986.txt">Table of n, a(n) for n = 0..60</a>

%p b:= proc(n, p) option remember; `if`(p[4]>n, 0, `if`(n=0, 1,

%p       add(add(add(add(b(n-1, sort(map(abs, p+[i, j, k, m])))

%p       , i=-1..1), j=-1..1), k=-1..1), m=-1..1)))

%p     end:

%p a:= n-> b(n, [0$2, 1$2]):

%p seq(a(n), n=0..20);  # _Alois P. Heinz_, Dec 02 2012

%t b[n_, p_] := b[n, p] = If[p[[4]] > n, 0, If[n == 0, 1,

%t      Sum[Sum[Sum[Sum[b[n-1, Sort[Abs[ p + {i, j, k, m}]]],

%t      {i, -1, 1}], {j, -1, 1}], {k, -1, 1}], {m, -1, 1}]]];

%t a[n_] := b[n, {0, 0, 1, 1}];

%t Table [a[n], {n, 0, 20}] (* _Jean-François Alcover_, Apr 28 2022, after _Alois P. Heinz_ *)

%o (JavaScript)

%o b=new Array();

%o for (i1=-1;i1<2;i1++)

%o for (i2=-1;i2<2;i2++)

%o for (i3=-1;i3<2;i3++)

%o for (i4=-1;i4<2;i4++) {

%o n=(i1+1)+(i2+1)*3+(i3+1)*9+(i4+1)*27;

%o b[n]=[i1,i2,i3,i4];

%o }

%o function inc(arr,m) {

%o al=arr.length-1;

%o full=true;

%o for (ac=0;ac<=al;ac++) if (arr[ac]!=m) {full=false;break;}

%o if (full==true) return false;

%o while (arr[al]==m && al>0) {arr[al]=0;al--;}

%o arr[al]++;

%o return true;

%o }

%o for (k=0;k<5;k++) {

%o c=0;

%o a=new Array();

%o for (i=0;i<k;i++) a[i]=0;

%o for (i=0;i<Math.pow(81,k);i++) {

%o p=[0,0,0,0];

%o 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];}

%o if (p[0]==1 && p[1]==0 && p[2]==0 && p[3]==1) c++;

%o inc(a,80);

%o }

%o document.write(c+", ");

%o }

%Y Cf. A219670, A219671.

%K nonn

%O 0,3

%A _Jon Perry_, Dec 02 2012

%E More terms from _Alois P. Heinz_, Dec 02 2012