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A285733 Transpose of square array A285732.

%I A285733 #18 Jun 12 2025 12:58:39
%S A285733 -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,
%T A285733 28,20,13,7,10,13,17,22,36,27,19,12,-5,14,18,23,29,45,35,26,18,11,15,
%U A285733 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
%N A285733 Transpose of square array A285732.
%C A285733 See A285732.
%H A285733 Antti Karttunen, <a href="/A285733/b285733.txt">Table of n, a(n) for n = 1..7260; the first 120 antidiagonals of the array</a>
%F A285733 A(n,k) = A285732(k,n) = A285723(n,k) - A286100(n,k).
%e A285733 The top left 9 X 9 corner of the array:
%e A285733   -1,  1,  3,  6, 10, 15, 21, 28, 36
%e A285733    1, -2,  2,  5,  9, 14, 20, 27, 35
%e A285733    2,  3, -3,  4,  8, 13, 19, 26, 34
%e A285733    4,  5,  6, -4,  7, 12, 18, 25, 33
%e A285733    7,  8,  9, 10, -5, 11, 17, 24, 32
%e A285733   11, 12, 13, 14, 15, -6, 16, 23, 31
%e A285733   16, 17, 18, 19, 20, 21, -7, 22, 30
%e A285733   22, 23, 24, 25, 26, 27, 28, -8, 29
%e A285733   29, 30, 31, 32, 33, 34, 35, 36, -9
%o A285733 (Scheme) (define (A285733 n) (A285732bi (A004736 n) (A002260 n))) ;; For A285732bi see under A285732.
%o A285733 (Python)
%o A285733 def T(n, m): return ((n + m)**2 - n - 3*m + 2)//2
%o A285733 def A(n, k): return -n if n == k else T(n - k, k) if n>k else T(n, k - n)
%o A285733 for n in range(1, 21): print([A(n - k + 1, k) for k in range(1, n + 1)]) # _Indranil Ghosh_, May 03 2017
%Y A285733 Transpose: A285732.
%Y A285733 Cf. A285723, A286100.
%K A285733 sign,tabl
%O A285733 1,4
%A A285733 _Antti Karttunen_, May 03 2017