Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #33 Mar 14 2015 11:43:30
%S 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,
%T 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,
%U 10,7,4,2,2,1,1,1,1,1,1,13,11,8,4,2,2
%N 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.
%C 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.
%C 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
%C 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
%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/pol001plt.jpg">Illustration of initial terms of the columns 0..10</a>
%e Illustration of initial terms of the 4th column:
%e ------------------------------------------------------
%e Level Graphic
%e ------------------------------------------------------
%e 10 *
%e 9 *
%e 8 *
%e 7 * *
%e 6 *
%e 5 *
%e 4 * * *
%e 3 *
%e 2 * * * *
%e 1 * * * * *
%e 0
%e -------------------------------------------------------
%e Column 4: 1,1,1,1,1,2,2,2,2,3,4,4,4,5,6,7,7,8,9,10,...
%e -------------------------------------------------------
%e Array begins:
%e 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...
%e 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,...
%e 3, 2, 1, 1, 1, 1, 1, 1, 1, 1,...
%e 4, 3, 2, 1, 1, 1, 1, 1, 1, 1,...
%e 5, 4, 2, 2, 1, 1, 1, 1, 1, 1,...
%e 6, 5, 3, 2, 2, 1, 1, 1, 1, 1,...
%e 7, 6, 4, 2, 2, 2, 1, 1, 1, 1,...
%e 8, 7, 5, 3, 2, 2, 2, 1, 1, 1,...
%e 9, 8, 6, 4, 2, 2, 2, 2, 1, 1,...
%p A000124i := proc(n)
%p local j;
%p for j from 0 do
%p if A000124(j) = n then
%p return j;
%p elif A000124(j) > n then
%p return -1 ;
%p end if;
%p end do:
%p end proc:
%p A210992 := proc(n,k)
%p local f,r,a,c;
%p f := k+1 ;
%p a := 1 ;
%p for r from 0 to n do
%p if f > 0 then
%p f := f-1;
%p else
%p a := a+1 ;
%p c := A000124i(a) ;
%p f := 0 ;
%p if c >= 0 then
%p f := max(0,k-c) ;
%p end if;
%p end if;
%p end do:
%p a ;
%p end proc: # _R. J. Mathar_, Jul 22 2012
%Y Columns 0-1: A000027, A028310.
%Y Cf. A000124, A195825, A210843, A210959, A211970.
%K nonn,tabl
%O 0,2
%A _Omar E. Pol_, Jun 30 2012