A087468 - OEIS

%I #14 Sep 25 2014 10:33:44

%S 1,3,2,7,5,4,12,10,8,6,19,16,14,11,9,27,24,21,18,15,13,37,33,30,26,23,

%T 20,17,48,44,40,36,32,29,25,22,61,56,52,47,43,39,35,31,28,75,70,65,60,

%U 55,51,46,42,38,34,91,85,80,74,69,64,59,54,50,45,41,108,102,96,90,84,79

%N Dispersion, read by antidiagonals, of the complement of row 0 of the array R in A087465.

%C The sequence is a permutation of the natural numbers and the array is a transposable dispersion.

%H Clark Kimberling and John E. Brown, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL7/Kimberling/kimber67.html">Partial Complements and Transposable Dispersions</a>, J. Integer Seqs., Vol. 7, 2004, Article 04.1.6, 22 pp.

%F Transpose of the array R in A087465.

%e Northwest corner of R:

%e 1 ... 3 ... 7 ... 12 .. 19

%e 2 ... 5 ... 10 .. 16 .. 24

%e 4 ... 8 ... 14 .. 21 .. 30

%e 6 ... 11 .. 18 .. 26 .. 36

%e 9 ... 15 .. 23 .. 32 .. 43

%e (See example at A087465.)

%t r = 20; r1 = 12;(*r=# rows of T,r1=# rows to show*);

%t c = 20; c1 = 12;(*c=# cols of T,c1=# cols to show*);

%t s[0] = 1; s[n_] := s[n] = s[n - 1] + 1 + Floor[3 n/2]; u = Table[s[n], {n, 0, 100}]

%t v = Complement[Range[Max[u]], u]; f[n_] := v[[n]]; Table[f[n], {n, 1, 30}]

%t mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1,   Length[Union[list]]]; rows = {NestList[f, 1, c]}; Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}]; w[i_, j_] := rows[[i, j]]; TableForm[Table[w[j, i], {i, 1, 10}, {j, 1, 10}]]   (*A087468 array*)

%t Flatten[Table[w[n - k + 1, k], {n, 1, c1}, {k, 1, n}]] (*A087468 sequence*)

%t TableForm[Table[w[j, 1] + w[1, i] + (i - 1)*(j - 1) - 1, {i, 1, 10}, {j, 1, 10}]] (*A087468 array,by formula*)

%Y Cf. A087465.

%K nonn,tabl

%O 0,2

%A _Clark Kimberling_, Sep 09 2003

%E Updated by _Clark Kimberling_, Sep 23 2014