OFFSET
0,2
COMMENTS
The sequence is a permutation of the natural numbers and the array is a transposable dispersion.
LINKS
Clark Kimberling and John E. Brown, Partial Complements and Transposable Dispersions, J. Integer Seqs., Vol. 7, 2004, Article 04.1.6, 22 pp.
FORMULA
Transpose of the array R in A087465.
EXAMPLE
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.)
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*)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Sep 09 2003
EXTENSIONS
Updated by Clark Kimberling, Sep 23 2014
STATUS
approved