A246694 Triangle t(n,k) = t(n,k-2) + 1 if n > 1 and 2 <= k <= n; t(0,0) = 1, t(1,0) = 1, t(1,1) = 2; if n > 1 is odd, then t(n,0) = t(n-1,n-2) + 1 and t(n,1) = t(n-1,n-1) + 1; if n > 1 is even, then t(n,0) = t(n-1,n-1) + 1 and t(n,1) = t(n-1,n-2) + 1.

1, 1, 2, 3, 2, 4, 3, 5, 4, 6, 7, 5, 8, 6, 9, 7, 10, 8, 11, 9, 12, 13, 10, 14, 11, 15, 12, 16, 13, 17, 14, 18, 15, 19, 16, 20, 21, 17, 22, 18, 23, 19, 24, 20, 25, 21, 26, 22, 27, 23, 28, 24, 29, 25, 30, 31, 26, 32, 27, 33, 28, 34, 29, 35, 30, 36, 31, 37, 32

Offset

0,3

Comments

As an array, for each m, row 2*m has m odd numbers and m+1 even numbers; row 2*m-1 has m odds and m evens. As a sequence, every positive integer n occurs exactly twice, separated by floor((n+1)/2) other numbers.

Links

Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened

Example

First 8 rows:
1
1 ... 2
3 ... 2 ... 4
3 ... 5 ... 4 ... 6
7 ... 5 ... 8 ... 6 ... 9
7 ... 10 .. 8 ... 11 .. 9 ... 12
13 .. 10 .. 14 .. 11 .. 15 .. 12 .. 16
13 .. 17 .. 14 .. 18 .. 15 .. 19 .. 16 .. 20

Mathematica

z = 25; t[0, 0] = 1; t[1, 0] = 1; t[1, 1] = 2;
t[n_, 0] := If[OddQ[n], t[n - 1, n - 2] + 1, t[n - 1, n - 1] + 1];
t[n_, 1] := If[OddQ[n], t[n - 1, n - 1] + 1, t[n - 1, n - 2] + 1];
t[n_, k_] := t[n, k - 2] + 1; Flatten[Table[t[n, k], {n, 0, z}, {k, 0, n}]](*A246694*)

Prog

(Haskell)
a246694 n k = a246694_tabl !! n !! k
a246694_row n = a246694_tabl !! n
a246694_tabl = [1] : [1, 2] : f 1 2 [1, 2] where
   f i z xs = ys : f j (z + 1) ys where
     ys = take (z + 1) $ map (+ 1) (xs !! (z - i) : xs !! (z - j) : ys)
     j = 3 - i
-- Reinhard Zumkeller, Sep 03 2014

Crossrefs

Cf. A246705, A246706, A246696.

Cf. A246695 (row sums), A174114 (central terms).

Sequence in context: A361000 A283368 A199474 * A054384 A026400 A026409

Adjacent sequences: A246691 A246692 A246693 * A246695 A246696 A246697

Keyword

nonn,easy,tabl

Author

Clark Kimberling, Sep 01 2014

Extensions

Edited by M. F. Hasler, Nov 17 2014

Status

approved