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A246690 Number A(n,k) of compositions of n into parts of the k-th list of distinct parts in the order given by A246688; square array A(n,k), n>=0, k>=0, read by antidiagonals. 3
1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 2, 0, 1, 0, 1, 1, 0, 3, 1, 1, 0, 1, 0, 1, 1, 5, 0, 1, 0, 1, 1, 0, 2, 0, 8, 1, 1, 0, 1, 0, 1, 0, 3, 0, 13, 0, 1, 0, 1, 0, 1, 1, 1, 4, 1, 21, 1, 1, 0, 1, 1, 0, 1, 2, 0, 6, 0, 34, 0, 1, 0, 1, 1, 2, 0, 1, 3, 0, 9, 0, 55, 1, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,18

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, Antidiagonals n = 0..140

EXAMPLE

Square array A(n,k) begins:

1, 1, 1,  1, 1,  1, 1,  1, 1, 1,   1, 1, 1, 1,   1, ...

0, 1, 0,  1, 0,  1, 0,  1, 0, 0,   1, 1, 0, 0,   1, ...

0, 1, 1,  2, 0,  1, 0,  1, 1, 0,   2, 1, 1, 0,   2, ...

0, 1, 0,  3, 1,  2, 0,  1, 1, 0,   4, 1, 0, 0,   3, ...

0, 1, 1,  5, 0,  3, 1,  2, 1, 0,   7, 1, 2, 0,   6, ...

0, 1, 0,  8, 0,  4, 0,  3, 2, 1,  13, 2, 0, 0,  10, ...

0, 1, 1, 13, 1,  6, 0,  4, 2, 0,  24, 3, 3, 1,  18, ...

0, 1, 0, 21, 0,  9, 0,  5, 3, 0,  44, 4, 0, 0,  31, ...

0, 1, 1, 34, 0, 13, 1,  7, 4, 0,  81, 5, 5, 0,  55, ...

0, 1, 0, 55, 1, 19, 0, 10, 5, 0, 149, 6, 0, 0,  96, ...

0, 1, 1, 89, 0, 28, 0, 14, 7, 1, 274, 8, 8, 0, 169, ...

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, k)-> g(n, f(k)):

seq(seq(A(n, d-n), n=0..d), d=0..14);

CROSSREFS

Columns k=0-21, 23, 25-28 give: A000007, A000012, A059841, A000045(n+1), A079978, A000930, A121262, A003269(n+1), A182097, A079998, A000073(n+2), A003520, A079977, A079979, A060945, A005708, A001687(n+1), A017817, A082784, A079971, A006498, A005709, A052920, A120400, A060961, A005710, A013979.

Main diagonal gives A246691.

Cf. A246688, A246720 (the same for partitions).

Sequence in context: A136745 A214157 A246720 * A317748 A090465 A052344

Adjacent sequences:  A246687 A246688 A246689 * A246691 A246692 A246693

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Sep 01 2014

STATUS

approved

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Last modified August 10 04:38 EDT 2020. Contains 336368 sequences. (Running on oeis4.)