OFFSET
0,2
COMMENTS
As an array, for each m, row 2*m has m even numbers and [(m+1)/2] odd numbers, and row 2*m-1 has m odds and m evens. Every positive number occurs exactly once, so that as a sequence (with offset 1), this is a permutation of the positive integers, with inverse A246698.
FORMULA
For m >= 0, {t(2*m,0)} = A001844. - Ruud H.G. van Tol, Sep 30 2024
EXAMPLE
First 8 rows:
1
2 ... 3
5 ... 4 ... 7
6 ... 9 ... 8 ... 11
13 .. 10 .. 15 .. 12 .. 17
14 .. 19 .. 16 .. 21 .. 18 .. 23
25 .. 20 .. 27 .. 22 .. 29 .. 24 .. 31
26 .. 33 .. 28 .. 35 .. 30 .. 37 .. 32 .. 39
MATHEMATICA
z = 25; t[0, 0] = 1; t[1, 0] = 2; t[1, 1] = 3; t[n_, 0] := t[n, 0] = If[OddQ[n], t[n - 1, n - 2] + 2, t[n - 1, n - 1] + 2]; t[n_, 1] := t[n, 1] = If[OddQ[n], t[n - 1, n - 1] + 2, t[n - 1, n - 2] + 2]; t[n_, k_] := t[n, k] = t[n, k - 2] + 2;
u = Flatten[Table[t[n, k], {n, 0, z}, {k, 0, n}]] (* A246696 *)
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Sep 17 2014
EXTENSIONS
Edited by M. F. Hasler, Nov 17 2014
STATUS
approved