A256507 Triangle read by rows, giving in triangle A256946 the positions of n-th's row terms in row n+1.

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

Offset: 1

Author

Reinhard Zumkeller, Apr 22 2015

Keywords

• nonn
• tabf

Comments

A256946(n+1,T(n,k),k) = A256946(n,k), k = 1..n*(n+2);

T(n,k) = k for k = 1..n;

T(n,n+1) = n + 3;

T(n,n*(n+2)) = (n+2)^2 - 2.

Examples

			.  n | T(n,*)             | A256946(n,*)
. ---+--------------------+--------------------------------------
.  1 | 1,4,7              | [1,            2,          3]
.  2 | 1,2,5,7,8,11,12,14 | [1,4,     5,   2,6,      7,3,   8]
.  3 | 1,2,3,6,7,9,11,... | [1,4,9,10,5,11,2,6,12,13,7,3,14,8,15] .
		

Links

• Reinhard Zumkeller, Rows n = 1..30 of triangle, flattened

Crossrefs

Cf. A005563 (row lengths), A256946.

Programs

Haskell

import Data.List (elemIndex); import Data.Maybe (fromJust)
a256507 n k = a256507_tabf !! (n-1) !! (k-1)
a256507_row n = a256507_tabf !! (n-1)
a256507_tabf = zipWith (\us vs ->
                       map ((+ 1) . fromJust . (`elemIndex` vs)) us)
                       a256946_tabf $ tail a256946_tabf

Mathematica

row[n_] := (* row of A256946 *) row[n] = SortBy[Range[n(n+2)], If[IntegerQ[ Sqrt[#]], 0, N[FractionalPart[Sqrt[#]]]]&];
T[n_, k_] := FirstPosition[row[n+1], row[n][[k]]][[1]];
Table[T[n, k], {n, 1, 5}, {k, 1, n(n+2)}] // Flatten (* Jean-François Alcover, Sep 17 2019 *)