A322326 Number of compositions of n in which at most one part has even multiplicity.

1, 1, 2, 4, 8, 16, 26, 64, 107, 226, 382, 859, 1488, 3124, 5628, 11326, 21629, 42274, 81420, 158002, 309129, 592798, 1181109, 2234319, 4501108, 8461706, 17211219, 32187953, 66018320, 122792362, 253549269, 469715744, 975300728, 1802165555, 3758679309, 6931995005

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Example

a(6) = 26: 111111, 11112, 11121, 11211, 12111, 21111, 222, 1113, 1131, 1311, 3111, 123, 132, 213, 231, 312, 321, 33, 114, 141, 411, 24, 42, 15, 51, 6.

Maple

b:= proc(n, i, p, t) option remember; `if`(n=0 or i=1, `if`(n>0 and
       t and n::even, 0, (n+p)!/n!), b(n, i-1, p, t)+add(`if`(t and
       j::even, 0, b(n-i*j, i-1, p+j, t or j::even))/j!, j=1..n/i))
    end:
a:= n-> b(n$2, 0, false):
seq(a(n), n=0..40);

Mathematica

b[n_, i_, p_, t_] := b[n, i, p, t] = If[n == 0 || i == 1, If[n > 0 &&
     t && EvenQ[n], 0, (n + p)!/n!], b[n, i - 1, p, t] + Sum[If[t &&
     EvenQ[j], 0, b[n - i*j, i-1, p+j, t || EvenQ[j]]]/j!, {j, 1, n/i}]];
a[n_] := b[n, n, 0, False];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Mar 05 2022, after Alois P. Heinz *)

Crossrefs

Cf. A130495, A242391, A322132.

Sequence in context: A319385 A180249 A060957 * A018826 A342130 A258624

Adjacent sequences: A322323 A322324 A322325 * A322327 A322328 A322329

Keyword

nonn

Author

Alois P. Heinz, Dec 03 2018

Status

approved