A237448 Square array T(row >= 1, col >= 1): The first row, row=1, T(1,col) = col = A000027. When row > col, T(row,col) = row, otherwise (when 1 < row <= col), T(row,col) = row-1.

1, 2, 2, 3, 1, 3, 4, 1, 3, 4, 5, 1, 2, 4, 5, 6, 1, 2, 4, 5, 6, 7, 1, 2, 3, 5, 6, 7, 8, 1, 2, 3, 5, 6, 7, 8, 9, 1, 2, 3, 4, 6, 7, 8, 9, 10, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13

Offset: 1

Author

Antti Karttunen, Feb 10 2014

Keywords

• nonn
• tabl
• easy

Comments

This is transpose of A237447, please see comments there.

Examples

			The top left 9 X 9 corner of this infinite square array:
  1 2 3 4 5 6 7 8 9
  2 1 1 1 1 1 1 1 1
  3 3 2 2 2 2 2 2 2
  4 4 4 3 3 3 3 3 3
  5 5 5 5 4 4 4 4 4
  6 6 6 6 6 5 5 5 5
  7 7 7 7 7 7 6 6 6
  8 8 8 8 8 8 8 7 7
  9 9 9 9 9 9 9 9 8
		

Links

• Antti Karttunen, Table of first 144 antidiagonals of array, flattened

Crossrefs

Transpose: A237447.

The leftmost column and the topmost row: A000027. Second row: A054977. Central diagonal: A028310 (note the different starting offsets).

Antidiagonal sums: A074148.

Cf. A237265, A000330, A002024, A002260, A004736, A000124, A010054.

Programs

Scheme

(define (A237448 n) (cond ((= 1 (A010054 (- n 1))) (A002024 n)) ((< (A004736 n) (A002260 n)) (A002260 n)) (else (- (A002260 n) 1))))

Formula

As a one-dimensional sequence:

If A010054(n-1) = 1 [that is, if n is in A000124], then a(n) = A002024(n), otherwise, if A004736(n) < A002260(n), a(n) = A002260(n), and if A004736(n) >= A002260(n), a(n) = A002260(n)-1.

Equivalently, as a square array T:

When col < row, T(row,col) = row, for 1 < row <= col, T(row,col) = row-1, and for the first row T(1,col) = col = A000027(col).

Can be computed also as a transposed version of the infinite limit of the finite square arrays in sequence A237265: T(row,col) = A237265((A000330(max(row,col)-1)+1) + (max(row,col)*(col-1)) + (row-1)).