A246691 Number of compositions of n into parts of the n-th list of distinct parts in the order given by A246688.

1, 1, 1, 3, 0, 4, 0, 5, 4, 0, 274, 11, 13, 0, 1601, 21, 11, 10, 0, 15571, 7921, 53, 41, 12, 1, 246441, 64208, 119, 16169, 47, 89, 35, 0, 1439975216, 17319590, 1835123, 956698, 531, 274291, 0, 82, 0, 0, 428262742476, 1923714115, 72992449, 20086406, 1915, 4051405

Offset

0,4

Comments

The first lists of distinct parts in the order given by A246688 are: 0:[], 1:[1], 2:[2], 3:[1,2], 4:[3], 5:[1,3], 6:[4], 7:[1,4], 8:[2,3], 9:[5], 10:[1,2,3], 11:[1,5], 12:[2,4], 13:[6], 14:[1,2,4], 15:[1,6], 16:[2,5], 17:[3,4], 18:[7], 19:[1,2,5], 20:[1,3,4], ... .

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1260

Formula

a(n) = A246690(n,n).

Example

a(7) = 5 because there are 5 compositions of 7 into parts 1, 4: [1,1,1,1,1,1,1], [1,1,1,4], [1,1,4,1], [1,4,1,1], [4,1,1,1].

Maple

b:= proc(n, i) b(n, i):= `if`(n=0, [[]], `if`(i>n, [],
      [map(x->[i, x[]], b(n-i, i+1))[], b(n, i+1)[]]))
    end:
f:= proc() local i, l; i, l:=0, [];
      proc(n) while n>=nops(l)
        do l:=[l[], b(i, 1)[]]; i:=i+1 od; l[n+1]
      end
    end():
g:= proc(n, l) option remember; `if`(n=0, 1,
      add(`if`(i>n, 0, g(n-i, l)), i=l))
    end:
a:= n-> g(n, f(n)):
seq(a(n), n=0..80);

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, {{}}, If[i > n, {}, Join[Prepend[#, i]& /@ b[n - i, i + 1], b[n, i + 1]]]];
f = Module[{i = 0, l = {}}, Function[n, While[n >= Length[l], l = Join[l, b[i, 1]]; i++]; l[[n + 1]]]];
g[n_, l_] := g[n, l] = If[n == 0, 1, Sum[If[i>n, 0, g[n - i, l]], {i, l}]];
a[n_] := g[n, f[n]];
Table[a[n], {n, 0, 80}] (* Jean-François Alcover, Jul 12 2021, after Alois P. Heinz *)

Crossrefs

Cf. A246688, A246690, A246721 (the same for partitions).

Sequence in context: A218859 A363028 A364067 * A066705 A277894 A027636

Adjacent sequences: A246688 A246689 A246690 * A246692 A246693 A246694

Keyword

nonn,look

Author

Alois P. Heinz, Sep 01 2014

Status

approved