A246696 Triangle t(n,k) = t(n,k-2) + 2 if n > 1 and 2 <= k <= n; t(0,0) = 1, t(1,0) = 2, t(1,1) = 3; if n > 1 is odd, then t(n,0) = t(n-1,n-2) + 2 and t(n,1) = t(n-1,n-1) + 2; if n > 1 is even, then t(n,0) = t(n-1,n-1) + 2 and t(n,1) = t(n-1,n-2) + 2.

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, 41, 34, 43, 36, 45, 38, 47, 40, 49, 42, 51, 44, 53, 46, 55, 48, 57, 50, 59, 61, 52, 63, 54, 65, 56, 67, 58, 69, 60, 71, 62

Offset: 0

Author

Clark Kimberling, Sep 17 2014

Keywords

• nonn
• easy
• tabl

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.

Examples

			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
		

Crossrefs

Cf. A246697 (row sums), A246698 (inverse permutation), A246694.

Cf. A001844, A047838 (main diagonal), A128174 (parity).

Programs

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 *)

Formula

For m >= 0, {t(2*m,0)} = A001844. - Ruud H.G. van Tol, Sep 30 2024

Extensions

Edited by M. F. Hasler, Nov 17 2014