A348478 Number of compositions of n into exactly n nonnegative parts such that each positive i-th part has the same parity as i.

1, 1, 1, 4, 7, 23, 55, 164, 407, 1235, 3051, 9432, 23431, 72989, 182624, 571384, 1436855, 4511979, 11387467, 35866100, 90782837, 286622226, 727226578, 2300578392, 5848776767, 18533394763, 47197285045, 149769168304, 381956145802, 1213526310665, 3098742448230

Offset: 0

Author

Alois P. Heinz, Oct 20 2021

Keywords

• nonn

Examples

			a(0) = 1: [].
a(1) = 1: [1].
a(2) = 1: [0,2].
a(3) = 4: [1,2,0], [0,2,1], [3,0,0], [0,0,3].
a(4) = 7: [1,2,1,0], [1,0,1,2], [3,0,1,0], [1,0,3,0], [0,2,0,2], [0,4,0,0], [0,0,0,4].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2169

Crossrefs

Cf. A001700, A062200, A088218, A122514, A165817, A305161, A324969, A348476.

Programs

Maple

b:= proc(n, t) option remember; `if`(t=0, 1-signum(n),
      add(`if`(j=0 or (t-j)::even, b(n-j, t-1), 0), j=0..n))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..33);

Mathematica

b[n_, t_] := b[n, t] = If[t == 0, 1 - Sign[n],
     Sum[If[j == 0 || EvenQ[t - j], b[n - j, t - 1], 0], {j, 0, n}]];
a[n_] :=  b[n, n];
Table[a[n], {n, 0, 33}] (* Jean-François Alcover, Apr 14 2022, after Alois P. Heinz *)