A087468 Dispersion, read by antidiagonals, of the complement of row 0 of the array R in A087465.

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, 20, 17, 48, 44, 40, 36, 32, 29, 25, 22, 61, 56, 52, 47, 43, 39, 35, 31, 28, 75, 70, 65, 60, 55, 51, 46, 42, 38, 34, 91, 85, 80, 74, 69, 64, 59, 54, 50, 45, 41, 108, 102, 96, 90, 84, 79

Offset: 0

Author

Clark Kimberling, Sep 09 2003

Keywords

• nonn
• tabl

Comments

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

Examples

			Northwest corner of R:
1 ... 3 ... 7 ... 12 .. 19
2 ... 5 ... 10 .. 16 .. 24
4 ... 8 ... 14 .. 21 .. 30
6 ... 11 .. 18 .. 26 .. 36
9 ... 15 .. 23 .. 32 .. 43
(See example at A087465.)
		

Links

• Clark Kimberling and John E. Brown, Partial Complements and Transposable Dispersions, J. Integer Seqs., Vol. 7, 2004, Article 04.1.6, 22 pp.

Crossrefs

Cf. A087465.

Programs

Mathematica

r = 20; r1 = 12;(*r=# rows of T,r1=# rows to show*);
c = 20; c1 = 12;(*c=# cols of T,c1=# cols to show*);
s[0] = 1; s[n_] := s[n] = s[n - 1] + 1 + Floor[3 n/2]; u = Table[s[n], {n, 0, 100}]
v = Complement[Range[Max[u]], u]; f[n_] := v[[n]]; Table[f[n], {n, 1, 30}]
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*)
Flatten[Table[w[n - k + 1, k], {n, 1, c1}, {k, 1, n}]] (*A087468 sequence*)
TableForm[Table[w[j, 1] + w[1, i] + (i - 1)*(j - 1) - 1, {i, 1, 10}, {j, 1, 10}]] (*A087468 array,by formula*)

Formula

Transpose of the array R in A087465.

Extensions

Updated by Clark Kimberling, Sep 23 2014