OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..2000
EXAMPLE
a(0) = 1: (), the empty composition.
a(1) = 1: [2].
a(3) = 2: [1,2,3], [3,2,1].
a(4) = 4: [1,2,3,2], [2,1,2,3], [2,3,2,1], [3,2,1,2].
a(5) = 2: [2,1,2,3,2], [2,3,2,1,2].
a(7) = 6: [1,2,1,2,3,2,3], [1,2,3,2,1,2,3], [1,2,3,2,3,2,1], [3,2,1,2,1,2,3], [3,2,1,2,3,2,1], [3,2,3,2,1,2,1].
MAPLE
b:= proc(n, i, k) option remember;
`if`(n<1 or i<1 or k<0 or 3/2*k>n, 0,
`if`(n=i, `if`(k=0, 1, 0),
add(b(n-i, i+j, k-1), j=[-1, 1])))
end:
a:= n-> `if`(n=0, 1, add(b(2*n, j, n-1), j=1..2*n)):
seq(a(n), n=0..48);
MATHEMATICA
b[n_, i_, k_] := b[n, i, k] = If[n < 1 || i < 1 || k < 0 || 3/2*k > n, 0, If[n == i, If[k == 0, 1, 0], Sum[b[n - i, i + j, k - 1], {j, {-1, 1}}]]];
a[n_] := If[n == 0, 1, Sum[b[2*n, j, n - 1], {j, 1, 2 n}]];
Table[a[n], {n, 0, 48}] (* Jean-François Alcover, Oct 27 2023, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 27 2023
STATUS
approved