A343853 Irregular triangle read by rows: the n-th row gives the row indices of the matrix of 1..n^2 filled successively back and forth along antidiagonals.

1, 1, 1, 2, 2, 1, 1, 2, 3, 2, 1, 2, 3, 3, 1, 1, 2, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 3, 4, 4, 1, 1, 2, 3, 2, 1, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 5, 4, 3, 4, 5, 5, 1, 1, 2, 3, 2, 1, 1, 2, 3, 4, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 3, 4, 5, 6, 6, 5, 4, 5, 6, 6

Offset

1,4

Links

Stefano Spezia, First 30 rows of the triangle, flattened

Example

The triangle begins:
1
1   1   2   2
1   1   2   3   2   1   2   3   3
1   1   2   3   2   1   1   2   3   4   4   3   2   3   4   4
...

Mathematica

a={}; For[n=1, n<=6, n++, For[d=1, d<=n, d++, If[OddQ[d], i=d; For [k=1, k<=d, k++, AppendTo[a, i-k+1]], i=1; For[k=1, k<=d, k++, AppendTo[a, i+k-1]]]]; For[d=n+1, d<=2n-1, d++, If[OddQ[d], i= n; For[k=1, k<=2n-d, k++, AppendTo[a, i-k+1]], If[EvenQ[d], i=d-n+1; For[k=1, k<=2n-d, k++, AppendTo[a, i+k-1]]]]]]; a

Crossrefs

Cf. A000290 (row length), A002411 (row sums), A060747 (number of antidiagonals), A078475, A319573, A343854 (column indices).

Sequence in context: A193596 A275420 A344961 * A143974 A301565 A237265

Adjacent sequences: A343850 A343851 A343852 * A343854 A343855 A343856

Keyword

nonn,look,tabf

Author

Stefano Spezia, May 01 2021

Status

approved