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

0,4

Links

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

Example

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].

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 *)

Crossrefs

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

Sequence in context: A101824 A270238 A027946 * A363543 A242315 A275313

Adjacent sequences: A348475 A348476 A348477 * A348479 A348480 A348481

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2021

Status

approved