A343558 Irregular triangle read by rows: the n-th row gives the row indices of the consecutive elements of the spiral of the n X n matrix defined in A126224.

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

Offset

1,4

Links

Stefano Spezia, First 30 rows of the triangle, flattened

Example

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

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=Ceiling[s/4]; For[i=1, i<=Ceiling[n-s/2], i++, AppendTo[a, k]], If[EvenQ[s]&&Mod[s, 4]==2, For[i=1, i<=Ceiling[n-s/2], i++, AppendTo[a, k+i]]; k+=Ceiling[n-s/2], If[EvenQ[s]&&Mod[s, 4]==0, For[i=1, i<=Ceiling[n-s/2], i++, AppendTo[a, k-i]]; k=k-i+1, For[i=1, i<=Ceiling[n-s/2], i++, AppendTo[a, k]]]]]]]; a

Crossrefs

Cf. A000290 (row length), A002265, A002411 (row sums), A010873, A060747, A126224, A343559 (column indices).

Sequence in context: A047070 A071127 A029381 * A297877 A027926 A114730

Adjacent sequences: A343555 A343556 A343557 * A343559 A343560 A343561

Keyword

nonn,look,tabf

Author

Stefano Spezia, Apr 19 2021

Status

approved