%I #9 May 03 2017 21:56:23

%S -1,4,6,2,-2,3,11,3,2,15,7,23,-3,27,10,22,30,39,43,35,28,16,12,31,-4,

%T 34,14,21,37,17,24,10,7,26,20,45,29,57,18,14,-5,12,19,65,36,56,68,81,

%U 19,26,24,18,89,77,66,46,38,69,109,20,-6,17,117,76,44,55,79,47,58,124,141,21,16,149,133,64,54,91,67,107,48,140,125,177,-7,185,132,150,53,119

%N Square array A(n,k) read by antidiagonals, A(n,n) = -n, otherwise, if n > k, A(n,k) = T(n XOR k,k), else A(n,k) = T(n,n XOR k), where T(n,k) is sequence A000027 considered as a two-dimensional table and XOR is bitwise-xor (A003987).

%C The array is read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

%H Antti Karttunen, <a href="/A286155/b286155.txt">Table of n, a(n) for n = 1..10585; the first 145 antidiagonals of array</a>

%H MathWorld, <a href="http://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a>

%F If n = k, A(n,k) = -n, if n > k, A(n,k) = T(A003987(n,k),k), otherwise [when n < k], A(n,k) = T(n,A003987(n,k)), where T(n,k) is sequence A000027 considered as a two-dimensional table, that is, as a pairing function from N x N to N.

%e The top left 1 .. 12 x 1 .. 12 corner of the array:

%e -1, 4, 2, 11, 7, 22, 16, 37, 29, 56, 46, 79

%e 6, -2, 3, 23, 30, 12, 17, 57, 68, 38, 47, 107

%e 3, 2, -3, 39, 31, 24, 18, 81, 69, 58, 48, 139

%e 15, 27, 43, -4, 10, 14, 19, 109, 124, 140, 157, 59

%e 10, 35, 34, 7, -5, 26, 20, 141, 125, 176, 158, 83

%e 28, 14, 26, 12, 24, -6, 21, 177, 196, 142, 159, 111

%e 21, 20, 19, 18, 17, 16, -7, 217, 197, 178, 160, 143

%e 45, 65, 89, 117, 149, 185, 225, -8, 36, 44, 53, 63

%e 36, 77, 76, 133, 132, 205, 204, 29, -9, 64, 54, 87

%e 66, 44, 64, 150, 186, 148, 184, 38, 58, -10, 55, 115

%e 55, 54, 53, 168, 167, 166, 165, 48, 47, 46, -11, 147

%e 91, 119, 151, 63, 87, 115, 147, 59, 83, 111, 143, -12

%o (Scheme)

%o (define (A286155 n) (A286155bi (A002260 n) (A004736 n)))

%o (define (A286155bi row col) (cond ((= row col) (- row)) ((> row col) (A000027bi (A003987bi row col) col)) (else (A000027bi row (A003987bi col row))))) ;; Where A003987bi implements bitwise-xor (A003987).

%o (define (A000027bi row col) (* (/ 1 2) (+ (expt (+ row col) 2) (- row) (- (* 3 col)) 2)))

%Y Cf. A003987, A091255.

%Y Cf. also arrays A285732, A286151, A286153.

%K sign,tabl

%O 1,2

%A _Antti Karttunen_, May 03 2017