OFFSET
0,3
COMMENTS
The array is read by descending antidiagonals as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...
LINKS
Eric Weisstein's World of Mathematics, Pairing Function
FORMULA
EXAMPLE
The top left 0 .. 12 x 0 .. 12 corner of the array:
0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78
2, 2, 11, 7, 22, 16, 37, 29, 56, 46, 79, 67, 106
5, 13, 5, 8, 38, 47, 23, 30, 80, 93, 57, 68, 138
9, 8, 7, 9, 58, 48, 39, 31, 108, 94, 81, 69, 174
14, 26, 42, 62, 14, 19, 25, 32, 140, 157, 175, 194, 82
20, 19, 52, 51, 16, 20, 41, 33, 176, 158, 215, 195, 110
27, 43, 25, 41, 23, 39, 27, 34, 216, 237, 177, 196, 142
35, 34, 33, 32, 31, 30, 29, 35, 260, 238, 217, 197, 178
44, 64, 88, 116, 148, 184, 224, 268, 44, 53, 63, 74, 86
54, 53, 102, 101, 166, 165, 246, 245, 46, 54, 87, 75, 114
65, 89, 63, 87, 185, 225, 183, 223, 57, 81, 65, 76, 146
77, 76, 75, 74, 205, 204, 203, 202, 69, 68, 67, 77, 182
90, 118, 150, 186, 86, 114, 146, 182, 82, 110, 142, 178, 90
MATHEMATICA
T[a_, b_]:=((a + b)^2 + 3a + b)/2; A[n_, k_]:=If[n>k, T[BitXor[n, k], k], T[n, BitXor[n, k]]]; Table[A[k, n - k ], {n, 0, 20}, {k, 0, n}] // Flatten (* Indranil Ghosh, May 20 2017 *)
PROG
(Scheme)
(define (A286151bi row col) (define (pairA001477bi a b) (/ (+ (expt (+ a b) 2) (* 3 a) b) 2)) (cond ((> row col) (pairA001477bi (A003987bi row col) col)) (else (pairA001477bi row (A003987bi col row))))) ;; Where A003987bi implements bitwise-xor (A003987).
(Python)
def T(a, b): return ((a + b)**2 + 3*a + b)//2
def A(n, k): return T(n^k, k) if n>k else T(n, n^k)
for n in range(21): print([A(k, n - k) for k in range(n + 1)]) # Indranil Ghosh, May 20 2017
CROSSREFS
Cf. A286153 (same array without row 0 and column 0).
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, May 03 2017
STATUS
approved