editing

proposed

Antti Karttunen, <a href="/A286145/b286145.txt">Table of n, a(n) for n = 0..10584; the first 145 antidiagonals of array</a>

Cf. A003987, A001477, A286108, A286109, A286150, A286151.

Antti Karttunen, <a href="/A286145/b286145.txt">Table of n, a(n) for n = 0..10584</a>

Transpose: A286147.

Cf. A046092 (row 0), A000096 (column 0), A000217 (main diagonal).

The top left 0 .. 12 x 0 .. 12 corner of the array:

0, 4, 12, 24, 40, 60, 84, 112, 144, 180, 220, 264, 312

2, 1, 18, 17, 50, 49, 98, 97, 162, 161, 242, 241, 338

5, 13, 3, 11, 61, 85, 59, 83, 181, 221, 179, 219, 365

9, 8, 7, 6, 73, 72, 71, 70, 201, 200, 199, 198, 393

14, 26, 42, 62, 10, 22, 38, 58, 222, 266, 314, 366, 218

20, 19, 52, 51, 16, 15, 48, 47, 244, 243, 340, 339, 240

27, 43, 25, 41, 23, 39, 21, 37, 267, 315, 265, 313, 263

35, 34, 33, 32, 31, 30, 29, 28, 291, 290, 289, 288, 287

44, 64, 88, 116, 148, 184, 224, 268, 36, 56, 80, 108, 140

54, 53, 102, 101, 166, 165, 246, 245, 46, 45, 94, 93, 158

65, 89, 63, 87, 185, 225, 183, 223, 57, 81, 55, 79, 177

77, 76, 75, 74, 205, 204, 203, 202, 69, 68, 67, 66, 197

90, 118, 150, 186, 86, 114, 146, 182, 82, 110, 142, 178, 78

allocated for Antti KarttunenSquare array read by antidiagonals: A(n,k) = T(n XOR k, k), where T(n,k) is sequence A001477 considered as a two-dimensional table, and XOR is bitwise-xor (A003987).

0, 4, 2, 12, 1, 5, 24, 18, 13, 9, 40, 17, 3, 8, 14, 60, 50, 11, 7, 26, 20, 84, 49, 61, 6, 42, 19, 27, 112, 98, 85, 73, 62, 52, 43, 35, 144, 97, 59, 72, 10, 51, 25, 34, 44, 180, 162, 83, 71, 22, 16, 41, 33, 64, 54, 220, 161, 181, 70, 38, 15, 23, 32, 88, 53, 65, 264, 242, 221, 201, 58, 48, 39, 31, 116, 102, 89, 77, 312, 241, 179, 200, 222, 47, 21, 30, 148, 101, 63, 76, 90

0,2

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), ...

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

A(n,k) = T(A003987(n,k), 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, ...].

(Scheme)

(define (A286145 n) (A286145bi (A002262 n) (A025581 n)))

(define (A286145bi row col) (let ((a (A003987bi row col)) (b col)) (/ (+ (expt (+ a b) 2) (* 3 a) b) 2))) ;; Where A003987bi implements bitwise-xor (A003987).

Cf. A003987, A001477, A286109, A286150.

allocated

nonn,tabl

Antti Karttunen, May 03 2017

approved

editing

allocated for Antti Karttunen

allocated

approved