A343854 Irregular triangle read by rows: the n-th row gives the column indices of the matrix of 1..n^2 filled successively back and forth along antidiagonals.

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

Offset

1,3

Links

Stefano Spezia, First 30 rows of the triangle, flattened

Example

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

Mathematica

a={}; For[n=1, n<=6, n++, For[d=1, d<=n, d++, If[EvenQ[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[EvenQ[d], i= n; For[k=1, k<=2n-d, k++, AppendTo[a, i-k+1]], If[OddQ[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, A319572, A343853 (row indices).

Sequence in context: A104248 A358359 A249973 * A069349 A167404 A280223

Adjacent sequences: A343851 A343852 A343853 * A343855 A343856 A343857

Keyword

nonn,look,tabf

Author

Stefano Spezia, May 01 2021

Status

approved