|
EXAMPLE
|
a(0) = 1: [(0,0,0,0)].
a(1) = 1: [(1,1,1,1),(0,1,1,1),(0,0,1,1),(0,0,0,1),(0,0,0,0)].
a(2) = 42: [(2,2,2,2),(0,2,2,2),(0,0,2,2),(0,0,0,2),(0,0,0,0)], ..., [(2,2,2,2),(1,2,2,2),(1,1,2,2),(1,1,1,2),(1,1,1,1),(0,1,1,1),(0,0,1,1),(0,0,0,1),(0,0,0,0)].
|
|
MAPLE
|
b:= proc(l) option remember; `if`(l[-1]=0, 1, add(add(b(subsop(
i=j, l)), j=`if`(i=1, 0, l[i-1])..l[i]-1), i=1..nops(l)))
end:
a:= n-> `if`(n=0, 1, b([n$4])):
seq(a(n), n=0..16);
# second Maple program:
a:= proc(n) option remember; `if`(n<4, [1, 1, 42, 3532][n+1], (
(n+2)*(176594184*n^7-1252171596*n^6+3635870170*n^5
-5627048591*n^4 +4990722596*n^3 -2520013645*n^2+664396290*n
-69572160) *(n+1)^2* a(n-1) -3*(n-2)*(n+1)*(350669592*n^8
-2376848760*n^7+6486604406*n^6-9505222590*n^5
+8466195947*n^4-4746390780*n^3+1536942539*n^2-253906050*n
+14945856) *a(n-2) +(n-3)*(1575354456*n^7-8934392532*n^6
+18759259714*n^5-19551471603*n^4 +12013819684*n^3
-4838385873*n^2+1019903146*n-96686592)*(n-2)^2 *a(n-3)
-5000*(n-4)*(139932*n^4-226356*n^3+87227*n^2-21684*n-1919)
*(n-3)^2 *(n-2)^3 *a(n-4)) / (2*(n+3)*(139932*n^4-786084*n^3
+1605887*n^2-1434934*n+473280)*(n+2)^2*(n+1)^3))
end:
seq(a(n), n=0..20);
|