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A246721 Number of partitions of n into parts of the n-th list of distinct parts in the order given by A246688. 3
1, 1, 1, 2, 0, 2, 0, 2, 2, 0, 14, 3, 4, 0, 20, 3, 2, 1, 0, 26, 24, 4, 4, 2, 1, 35, 31, 4, 24, 2, 6, 1, 0, 378, 54, 42, 42, 5, 31, 0, 2, 0, 0, 631, 78, 61, 56, 5, 45, 34, 3, 3, 2, 2, 0, 1045, 992, 110, 85, 75, 73, 6, 55, 0, 7, 42, 8, 0, 2, 0, 1772, 1581, 156 (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..5000

FORMULA

a(n) = A246720(n,n).

EXAMPLE

a(7) = 2 because there are 2 partitions of 7 into parts 1, 4: [1,1,1,1,1,1,1], [1,1,1,4].

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, `if`(l=[], 0,

      add(g(n-l[-1]*j, subsop(-1=NULL, l)), j=0..n/l[-1])))

    end:

a:= n-> g(n, f(n)):

seq(a(n), n=0..80);

CROSSREFS

Main diagonal of A246720.

Cf. A246688, A246691 (the same for compositions).

Sequence in context: A204173 A103668 A276812 * A249441 A076472 A161840

Adjacent sequences:  A246718 A246719 A246720 * A246722 A246723 A246724

KEYWORD

nonn,look

AUTHOR

Alois P. Heinz, Sep 02 2014

STATUS

approved

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Last modified September 25 23:23 EDT 2020. Contains 337346 sequences. (Running on oeis4.)