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A286150 Square array read by antidiagonals: A(n,k) = T(n XOR k, min(n,k)), where T(n,k) is sequence A001477 considered as a two-dimensional table, and XOR is bitwise-xor (A003987). 6
0, 2, 2, 5, 1, 5, 9, 13, 13, 9, 14, 8, 3, 8, 14, 20, 26, 7, 7, 26, 20, 27, 19, 42, 6, 42, 19, 27, 35, 43, 52, 62, 62, 52, 43, 35, 44, 34, 25, 51, 10, 51, 25, 34, 44, 54, 64, 33, 41, 16, 16, 41, 33, 64, 54, 65, 53, 88, 32, 23, 15, 23, 32, 88, 53, 65, 77, 89, 102, 116, 31, 39, 39, 31, 116, 102, 89, 77, 90, 76, 63, 101, 148, 30, 21, 30, 148, 101, 63, 76, 90 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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
A(n,k) = T(A003987(n,k), min(n,k)), where T(n,k) is sequence A001477 considered as a two-dimensional table, that is, as a pairing function from [0, 1, 2, 3, ...] x [0, 1, 2, 3, ...] to [0, 1, 2, 3, ...].
EXAMPLE
The top left 0 .. 12 x 0 .. 12 corner of the array:
0, 2, 5, 9, 14, 20, 27, 35, 44, 54, 65, 77, 90
2, 1, 13, 8, 26, 19, 43, 34, 64, 53, 89, 76, 118
5, 13, 3, 7, 42, 52, 25, 33, 88, 102, 63, 75, 150
9, 8, 7, 6, 62, 51, 41, 32, 116, 101, 87, 74, 186
14, 26, 42, 62, 10, 16, 23, 31, 148, 166, 185, 205, 86
20, 19, 52, 51, 16, 15, 39, 30, 184, 165, 225, 204, 114
27, 43, 25, 41, 23, 39, 21, 29, 224, 246, 183, 203, 146
35, 34, 33, 32, 31, 30, 29, 28, 268, 245, 223, 202, 182
44, 64, 88, 116, 148, 184, 224, 268, 36, 46, 57, 69, 82
54, 53, 102, 101, 166, 165, 246, 245, 46, 45, 81, 68, 110
65, 89, 63, 87, 185, 225, 183, 223, 57, 81, 55, 67, 142
77, 76, 75, 74, 205, 204, 203, 202, 69, 68, 67, 66, 178
90, 118, 150, 186, 86, 114, 146, 182, 82, 110, 142, 178, 78
MATHEMATICA
T[a_, b_]:=((a + b)^2 + 3a + b)/2; A[n_, k_]:=T[BitXor[n, k], Min[n, k]]; Table[A[k, n - k], {n, 0, 20}, {k, 0, n}] // Flatten (* Indranil Ghosh, May 21 2017 *)
PROG
(Scheme)
(define (A286150 n) (A286150bi (A002262 n) (A025581 n)))
(define (A286150bi row col) (let ((a (A003987bi row col)) (b (min col row))) (/ (+ (expt (+ a b) 2) (* 3 a) b) 2))) ;; 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, min(n, k))
for n in range(21): print([A(k, n - k) for k in range(n + 1)]) # Indranil Ghosh, May 21 2017
CROSSREFS
Cf. A000096 (row 0 & column 0), A000217 (main diagonal).
Sequence in context: A079301 A079300 A128932 * A071950 A274847 A165922
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, May 03 2017
STATUS
approved

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Last modified March 29 03:39 EDT 2024. Contains 371264 sequences. (Running on oeis4.)