A285733 Transpose of square array A285732.

-1, 1, 1, 3, -2, 2, 6, 2, 3, 4, 10, 5, -3, 5, 7, 15, 9, 4, 6, 8, 11, 21, 14, 8, -4, 9, 12, 16, 28, 20, 13, 7, 10, 13, 17, 22, 36, 27, 19, 12, -5, 14, 18, 23, 29, 45, 35, 26, 18, 11, 15, 19, 24, 30, 37, 55, 44, 34, 25, 17, -6, 20, 25, 31, 38, 46, 66, 54, 43, 33, 24, 16, 21, 26, 32, 39, 47, 56, 78, 65, 53, 42, 32, 23, -7, 27, 33, 40, 48, 57, 67

Offset: 1

Author

Antti Karttunen, May 03 2017

Keywords

• sign
• tabl

Comments

See A285732.

Examples

			The top left 9 X 9 corner of the array:
  -1,  1,  3,  6, 10, 15, 21, 28, 36
   1, -2,  2,  5,  9, 14, 20, 27, 35
   2,  3, -3,  4,  8, 13, 19, 26, 34
   4,  5,  6, -4,  7, 12, 18, 25, 33
   7,  8,  9, 10, -5, 11, 17, 24, 32
  11, 12, 13, 14, 15, -6, 16, 23, 31
  16, 17, 18, 19, 20, 21, -7, 22, 30
  22, 23, 24, 25, 26, 27, 28, -8, 29
  29, 30, 31, 32, 33, 34, 35, 36, -9
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..7260; the first 120 antidiagonals of the array

Crossrefs

Transpose: A285732.

Cf. A285723, A286100.

Programs

Python

def T(n, m): return ((n + m)**2 - n - 3*m + 2)//2
def A(n, k): return -n if n == k else T(n - k, k) if n>k else T(n, k - n)
for n in range(1, 21): print([A(n - k + 1, k) for k in range(1, n + 1)]) # Indranil Ghosh, May 03 2017

Scheme

(define (A285733 n) (A285732bi (A004736 n) (A002260 n))) ;; For A285732bi see under A285732.

Formula

A(n,k) = A285732(k,n) = A285723(n,k) - A286100(n,k).