A343559 Irregular triangle read by rows: the n-th row gives the column indices of the consecutive elements of the spiral of the n X n matrix defined in A126224.

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

Offset

1,3

Links

Stefano Spezia, First 30 rows of the triangle, flattened

Example

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

Mathematica

a:={}; nmax:=6; For[n=1, n<=nmax, n++, For[s=1, s<=2n-1, s++, If[OddQ[s]&&Mod[s, 4]==1 , k=Floor[s/4]; For[i=1, i<=Ceiling[n-s/2], i++, AppendTo[a, k+i]]; k=+Floor[s/4]+Ceiling[n-s/2], If[EvenQ[s], For[i=1, i<=Ceiling[n-s/2], i++, AppendTo[a, k]], For[i=1, i<=Ceiling[n-s/2], i++, AppendTo[a, k-i]]; k=k-i+1]]]]; a

Crossrefs

Cf. A000290 (row length), A002265, A002411 (row sums), A010873, A060747, A126224, A343558 (row indices).

Sequence in context: A004739 A156282 A203776 * A242357 A120423 A113137

Adjacent sequences: A343556 A343557 A343558 * A343560 A343561 A343562

Keyword

nonn,look,tabf

Author

Stefano Spezia, Apr 19 2021

Status

approved