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%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
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