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A246691 Number of compositions of n into parts of the n-th list of distinct parts in the order given by A246688. 3
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Jul 12 2021, after Alois P. Heinz *)

CROSSREFS

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

Sequence in context: A308717 A297217 A218859 * A066705 A277894 A027636

Adjacent sequences:  A246688 A246689 A246690 * A246692 A246693 A246694

KEYWORD

nonn,look

AUTHOR

Alois P. Heinz, Sep 01 2014

STATUS

approved

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Last modified August 10 07:42 EDT 2022. Contains 356029 sequences. (Running on oeis4.)