A210992 Square array read by antidiagonals, in which column k starts with k plateaus of lengths k+1, k, k-1, k-2, k-3,..2 and of levels A000124: 1, 2, 4, 7, 11..., if k >= 1, connected by consecutive integers. After the last plateau the length remains 1.

1, 2, 1, 3, 1, 1, 4, 2, 1, 1, 5, 3, 1, 1, 1, 6, 4, 2, 1, 1, 1, 7, 5, 2, 1, 1, 1, 1, 8, 6, 3, 2, 1, 1, 1, 1, 9, 7, 4, 2, 1, 1, 1, 1, 1, 10, 8, 5, 2, 2, 1, 1, 1, 1, 1, 11, 9, 6, 3, 2, 1, 1, 1, 1, 1, 1, 12, 10, 7, 4, 2, 2, 1, 1, 1, 1, 1, 1, 13, 11, 8, 4, 2, 2

Offset

0,2

Comments

Column k contains k plateaus whose levels are the first k terms of A000124, therefore A000124(i) is the level of the i-th plateau of the column k when k -> infinity.

Column k contains the integers s>=1 repeated f(s) times, sorted, where f(s)=1 if s is not in A000124, otherwise, if A000124(c)=s, repeated f(s)=max(1,k+1-c) times. - R. J. Mathar, Jul 22 2012

It appears that this array can be represented by a structure in which the number of relevant nodes give A000005 (see also A210959). - Omar E. Pol, Jul 24 2012

Links

Table of n, a(n) for n=0..83.

Omar E. Pol, Illustration of initial terms of the columns 0..10

Example

Illustration of initial terms of the 4th column:
------------------------------------------------------
Level    Graphic
------------------------------------------------------
10                                              *
9                                             *
8                                           *
7                                       * *
6                                     *
5                                   *
4                             * * *
3                           *
2                   * * * *
1         * * * * *
0
-------------------------------------------------------
Column 4: 1,1,1,1,1,2,2,2,2,3,4,4,4,5,6,7,7,8,9,10,...
-------------------------------------------------------
Array begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...
2, 1, 1, 1, 1, 1, 1, 1, 1, 1,...
3, 2, 1, 1, 1, 1, 1, 1, 1, 1,...
4, 3, 2, 1, 1, 1, 1, 1, 1, 1,...
5, 4, 2, 2, 1, 1, 1, 1, 1, 1,...
6, 5, 3, 2, 2, 1, 1, 1, 1, 1,...
7, 6, 4, 2, 2, 2, 1, 1, 1, 1,...
8, 7, 5, 3, 2, 2, 2, 1, 1, 1,...
9, 8, 6, 4, 2, 2, 2, 2, 1, 1,...

Maple

A000124i := proc(n)
    local j;
    for j from 0 do
        if A000124(j) = n then
            return j;
        elif A000124(j) > n then
            return -1 ;
        end if;
    end do:
end proc:
A210992 := proc(n, k)
    local f, r, a, c;
    f := k+1  ;
    a := 1 ;
    for r from 0 to n do
        if f > 0 then
            f := f-1;
        else
            a := a+1 ;
            c := A000124i(a) ;
            f := 0 ;
            if c >= 0 then
                f := max(0, k-c) ;
            end if;
        end if;
    end do:
    a ;
end proc: # R. J. Mathar, Jul 22 2012

Crossrefs

Columns 0-1: A000027, A028310.

Cf. A000124, A195825, A210843, A210959, A211970.

Sequence in context: A174557 A010766 A135841 * A220484 A174066 A089178

Adjacent sequences: A210989 A210990 A210991 * A210993 A210994 A210995

Keyword

nonn,tabl

Author

Omar E. Pol, Jun 30 2012

Status

approved