OFFSET
0,5
LINKS
EXAMPLE
a(5) = 5:
: o o o o o
: | | / \ /|\ /( )\
: o o o o o o o o o o o
: / \ /|\ | | |
: o o o o o o o o
: |
: o
MAPLE
b:= proc(n, i, h, v) option remember; `if`(n=0, `if`(v=0, 1, 0),
`if`(i<1 or v<1 or n<v, 0, `if`(n=v, 1, add(binomial(j-1+
A(i, h), j)*b(n-i*j, i-1, h, v-j), j=0..min(n/i, v)))))
end:
A:= proc(n, k) option remember; `if`(n=0, 0,
add(`if`(j=k, 0, b(n-1$2, j$2)), j=0..n-1))
end:
a:= n-> A(n, n):
seq(a(n), n=0..40);
MATHEMATICA
b[n_, i_, h_, v_] := b[n, i, h, v] = If[n==0, If[v==0, 1, 0], If[i<1 || v<1 || n<v, 0, If[n==v, 1, Sum[Binomial[j-1+A[i, h], j]*b[n-i*j, i-1, h, v-j], {j, 0, Min[n/i, v]}]]]]; A[n_, k_] := A[n, k] = If[n==0, 0, Sum[If[ j==k, 0, b[n-1, n-1, j, j]], {j, 0, n-1}]]; a[n_] := A[n, n]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Feb 21 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 23 2015
STATUS
approved