OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..250
FORMULA
a(n) ~ 3^(3*n+3/2) / (4*Pi*n)^(3/2). - Vaclav Kotesovec, Sep 07 2014
Recurrence (of order 4): (n-1)^2*n^2*(n+1)*(2*n-5)*(7*n^4 - 56*n^3 + 166*n^2 - 216*n + 105)*a(n) = (n-1)*n*(2*n-5)*(2*n-1)*(70*n^6 - 630*n^5 + 2206*n^4 - 3759*n^3 + 3181*n^2 - 1188*n + 144)*a(n-1) + 3*(n-1)*(2*n-3)*(490*n^8 - 5880*n^7 + 30030*n^6 - 85050*n^5 + 145359*n^4 - 152064*n^3 + 93599*n^2 - 30264*n + 3852)*a(n-2) - 27*(n-2)^2*(2*n-5)*(2*n-1)*(70*n^6 - 630*n^5 + 2206*n^4 - 3813*n^3 + 3424*n^2 - 1563*n + 342)*a(n-3) - 729*(n-3)^3*(n-2)^2*(2*n-1)*(7*n^4 - 28*n^3 + 40*n^2 - 24*n + 6)*a(n-4). - Vaclav Kotesovec, Sep 07 2014
MAPLE
a:= proc(n) a(n):= `if`(n<6, [0, 1, 18, 294, 5776, 117045][n+1],
(n*(n-1)*(453658*n^4-2664929*n^3+6608535*n^2-8353208*n+3876664)
*a(n-1) +3*(n-1)*(286527*n^5+2962040*n^4-19850405*n^3+25517846
*n^2+20905560*n-41336424) *a(n-2) -18*(n-2)*(2*n-5)*(1294945*n^4
-12949450*n^3+54428897*n^2-110276360*n+88672932) *a(n-3) -81*(n-3)
*(286527*n^5-10125215*n^4+111022145*n^3-530226521*n^2+1163720520*n
-966508776) *a(n-4) +729*(453658*n^4-6408231*n^3+34683300*n^2
-84691467*n+77744124)*(n-4)^2 *a(n-5) +19683*(-42552+15593*n)
*(n-4)^2 *(n-5)^3 *a(n-6))/ (n^2*(n+1)*(n-1)^2*(15593*n-35413)))
end:
seq (a(n), n=0..30); # Alois P. Heinz, Nov 28 2012
A005717 := n -> simplify(GegenbauerC(n-1, -n, -1/2));
A002426 := n -> simplify(GegenbauerC(n, -n, -1/2));
PROG
(JavaScript)
b=[[1, 1, 1], [1, 1, 0], [1, 1, -1], [1, 0, 1], [1, 0, 0], [1, 0, -1], [1, -1, 1], [1, -1, 0], [1, -1, -1],
[0, 1, 1], [0, 1, 0], [0, 1, -1], [0, 0, 1], [0, 0, 0], [0, 0, -1], [0, -1, 1], [0, -1, 0], [0, -1, -1],
[-1, 1, 1], [-1, 1, 0], [-1, 1, -1], [-1, 0, 1], [-1, 0, 0], [-1, 0, -1], [-1, -1, 1], [-1, -1, 0], [-1, -1, -1]];
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<6; k++) {
c=0;
a=new Array();
for (i=0; i<k; i++) a[i]=0;
for (i=0; i<Math.pow(27, k); i++) {
p=[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]; }
if (p[0]==1 && p[1]==0 && p[2]==0) c++;
inc(a, 26);
}
document.write(c+", ");
}
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon Perry, Nov 24 2012
EXTENSIONS
More terms from Alois P. Heinz, Nov 28 2012
STATUS
approved