A286151 -id:A286151 - cp's OEIS frontend

A286108 Square array read by antidiagonals: A(n,k) = T(2*(n AND k), n XOR k), where T(n,k) is sequence A001477 considered as a two-dimensional table, AND is bitwise-and (A004198) and XOR is bitwise-xor (A003987).

0, 1, 1, 3, 5, 3, 6, 6, 6, 6, 10, 12, 14, 12, 10, 15, 15, 19, 19, 15, 15, 21, 23, 21, 27, 21, 23, 21, 28, 28, 28, 28, 28, 28, 28, 28, 36, 38, 40, 38, 44, 38, 40, 38, 36, 45, 45, 49, 49, 53, 53, 49, 49, 45, 45, 55, 57, 55, 61, 63, 65, 63, 61, 55, 57, 55, 66, 66, 66, 66, 74, 74, 74, 74, 66, 66, 66, 66, 78, 80, 82, 80, 78, 88, 90, 88, 78, 80, 82, 80, 78

Offset: 0

Antti Karttunen, May 03 2017

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), ...

			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
   1,  5,   6,  12,  15,  23,  28,  38,  45,  57,  66,  80,  91
   3,  6,  14,  19,  21,  28,  40,  49,  55,  66,  82,  95, 105
   6, 12,  19,  27,  28,  38,  49,  61,  66,  80,  95, 111, 120
  10, 15,  21,  28,  44,  53,  63,  74,  78,  91, 105, 120, 144
  15, 23,  28,  38,  53,  65,  74,  88,  91, 107, 120, 138, 161
  21, 28,  40,  49,  63,  74,  90, 103, 105, 120, 140, 157, 179
  28, 38,  49,  61,  74,  88, 103, 119, 120, 138, 157, 177, 198
  36, 45,  55,  66,  78,  91, 105, 120, 152, 169, 187, 206, 226
  45, 57,  66,  80,  91, 107, 120, 138, 169, 189, 206, 228, 247
  55, 66,  82,  95, 105, 120, 140, 157, 187, 206, 230, 251, 269
  66, 80,  95, 111, 120, 138, 157, 177, 206, 228, 251, 275, 292
  78, 91, 105, 120, 144, 161, 179, 198, 226, 247, 269, 292, 324

Antti Karttunen, Table of n, a(n) for n = 0..10584; the first 145 antidiagonals of array
Eric Weisstein's World of Mathematics, Pairing Function

Cf. A000217 (row 0 & column 0), A014106 (main diagonal).
Cf. A003056, A003987, A004198.
Cf. also arrays A286098, A286109, A286145, A286147, A286150, A286151.

T[a_, b_]:=((a + b)^2 + 3a + b)/2; A[n_, k_]:=T[2*BitAnd[n, k], BitXor[n, k]]; Table[A[k, n - k ], {n, 0, 20}, {k, 0, n}] // Flatten (* Indranil Ghosh, May 20 2017 *)

def T(a, b): return ((a + b)**2 + 3*a + b)//2
def A(n, k): return T(2*(n&k), n^k)
for n in range(21): print([A(k, n - k) for k in range(n + 1)]) # Indranil Ghosh, May 20 2017

(define (A286108 n) (A286108bi (A002262 n) (A025581 n)))
(define (A286108bi row col) (let ((a (* 2 (A004198bi row col))) (b (A003987bi row col))) (/ (+ (expt (+ a b) 2) (* 3 a) b) 2))) ;; Here A003987bi and A004198bi implement bitwise-xor (A003987) and bitwise-and (A004198).

A(n,k) = T(2*A004198(n,k), A003987(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, ...].

A286109 Square array read by antidiagonals: A(n,k) = T(n XOR k, 2*(n AND k)), where T(n,k) is sequence A001477 considered as a two-dimensional table, AND is bitwise-and (A004198) and XOR is bitwise-xor (A003987).

Original entry on oeis.org

0, 2, 2, 5, 3, 5, 9, 9, 9, 9, 14, 12, 10, 12, 14, 20, 20, 16, 16, 20, 20, 27, 25, 27, 21, 27, 25, 27, 35, 35, 35, 35, 35, 35, 35, 35, 44, 42, 40, 42, 36, 42, 40, 42, 44, 54, 54, 50, 50, 46, 46, 50, 50, 54, 54, 65, 63, 65, 59, 57, 55, 57, 59, 65, 63, 65, 77, 77, 77, 77, 69, 69, 69, 69, 77, 77, 77, 77, 90, 88, 86, 88, 90, 80, 78, 80, 90, 88, 86, 88, 90

Offset: 0

Antti Karttunen, May 03 2017

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), ...

			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,   3,   9,  12,  20,  25,  35,  42,  54,  63,  77,  88, 104
   5,   9,  10,  16,  27,  35,  40,  50,  65,  77,  86, 100, 119
   9,  12,  16,  21,  35,  42,  50,  59,  77,  88, 100, 113, 135
  14,  20,  27,  35,  36,  46,  57,  69,  90, 104, 119, 135, 144
  20,  25,  35,  42,  46,  55,  69,  80, 104, 117, 135, 150, 162
  27,  35,  40,  50,  57,  69,  78,  92, 119, 135, 148, 166, 181
  35,  42,  50,  59,  69,  80,  92, 105, 135, 150, 166, 183, 201
  44,  54,  65,  77,  90, 104, 119, 135, 136, 154, 173, 193, 214
  54,  63,  77,  88, 104, 117, 135, 150, 154, 171, 193, 212, 236
  65,  77,  86, 100, 119, 135, 148, 166, 173, 193, 210, 232, 259
  77,  88, 100, 113, 135, 150, 166, 183, 193, 212, 232, 253, 283
  90, 104, 119, 135, 144, 162, 181, 201, 214, 236, 259, 283, 300

Antti Karttunen, Table of n, a(n) for n = 0..10584; the first 145 antidiagonals of array
Eric Weisstein's World of Mathematics, Pairing Function

Cf. A000096 (row 0 & column 0), A014105 (main diagonal).
Cf. A003056, A003987, A004198.
Cf. also arrays A286099, A286108, A286145, A286147, A286150, A286151.

T[a_, b_]:=((a + b)^2 + 3a + b)/2; A[n_, k_]:=T[BitXor[n, k], 2*BitAnd[n, k]]; Table[A[k, n - k ], {n, 0, 20}, {k, 0, n}] // Flatten (* Indranil Ghosh, May 20 2017 *)

def T(a, b): return ((a + b)**2 + 3*a + b)//2
def A(n, k): return T(n^k, 2*(n&k))
for n in range(21): print([A(k, n - k) for k in range(n + 1)]) # Indranil Ghosh, May 20 2017

(define (A286109 n) (A286109bi (A002262 n) (A025581 n)))
(define (A286109bi row col) (let ((a (A003987bi row col)) (b (* 2 (A004198bi row col)))) (/ (+ (expt (+ a b) 2) (* 3 a) b) 2))) ;; Here A003987bi and A004198bi implement bitwise-xor (A003987) and bitwise-and (A004198).

A(n,k) = T(A003987(n,k), 2*A004198(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, ...].

A286145 Square 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).

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, May 03 2017

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), ...

			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

Antti Karttunen, Table of n, a(n) for n = 0..10584; the first 145 antidiagonals of array
MathWorld, Pairing Function

Transpose: A286147.
Cf. A046092 (row 0), A000096 (column 0), A000217 (main diagonal).
Cf. A003987, A001477, A286108, A286109, A286150, A286151.

T[a_, b_]:=((a + b)^2 + 3a + b)/2; A[n_, k_]:=T[BitXor[n, k], k]; Table[A[k, n - k ], {n, 0, 20}, {k, 0, n}] // Flatten (* Indranil Ghosh, May 21 2017 *)

def T(a, b): return ((a + b)**2 + 3*a + b)//2
def A(n, k): return T(n^k, k)
for n in range(21): print([A(k, n - k) for k in range(n + 1)]) # Indranil Ghosh, May 21 2017

(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).

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, ...].

A286147 Square array read by antidiagonals: A(n,k) = T(n XOR k, n), where T(n,k) is sequence A001477 considered as a two-dimensional table, and XOR is bitwise-xor (A003987).

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, May 03 2017

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), ...

			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
    4,   1,  13,   8,  26,  19,  43,  34,  64,  53,  89,  76, 118
   12,  18,   3,   7,  42,  52,  25,  33,  88, 102,  63,  75, 150
   24,  17,  11,   6,  62,  51,  41,  32, 116, 101,  87,  74, 186
   40,  50,  61,  73,  10,  16,  23,  31, 148, 166, 185, 205,  86
   60,  49,  85,  72,  22,  15,  39,  30, 184, 165, 225, 204, 114
   84,  98,  59,  71,  38,  48,  21,  29, 224, 246, 183, 203, 146
  112,  97,  83,  70,  58,  47,  37,  28, 268, 245, 223, 202, 182
  144, 162, 181, 201, 222, 244, 267, 291,  36,  46,  57,  69,  82
  180, 161, 221, 200, 266, 243, 315, 290,  56,  45,  81,  68, 110
  220, 242, 179, 199, 314, 340, 265, 289,  80,  94,  55,  67, 142
  264, 241, 219, 198, 366, 339, 313, 288, 108,  93,  79,  66, 178
  312, 338, 365, 393, 218, 240, 263, 287, 140, 158, 177, 197,  78

Antti Karttunen, Table of n, a(n) for n = 0..10584; the first 145 antidiagonals of array
MathWorld, Pairing Function

Transpose: A286145.
Cf. A000096 (row 0), A046092 (column 0), A000217 (main diagonal).
Cf. A003987, A001477, A286108, A286109, A286150, A286151.

T[a_, b_]:=((a + b)^2 + 3a + b)/2; A[n_, k_]:=T[BitXor[n, k], k]; Table[A[n - k, k], {n, 0, 20}, {k, 0, n}] // Flatten (* Indranil Ghosh, May 21 2017 *)

def T(a, b): return ((a + b)**2 + 3*a + b)//2
def A(n, k): return T(n^k, k)
for n in range(21): print([A(n - k, k) for k in range(n + 1)]) # Indranil Ghosh, May 21 2017

(define (A286147 n) (A286147bi (A002262 n) (A025581 n)))
(define (A286147bi row col) (let ((a (A003987bi row col)) (b row)) (/ (+ (expt (+ a b) 2) (* 3 a) b) 2))) ;; Where A003987bi implements bitwise-xor (A003987).

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

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).

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, May 03 2017

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), ...

			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

Antti Karttunen, Table of n, a(n) for n = 0..10584; the first 145 antidiagonals of array
Eric Weisstein's World of Mathematics, Pairing Function

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

Cf. A003987, A001477, A286108, A286109, A286145, A286147, A286151.

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 *)

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

(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).

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, ...].

A286153 Square array read by descending antidiagonals A(1,1), A(1,2), A(2,1), ...: If n > k, A(n,k) = T(n XOR k, k), and otherwise A(n,k) = T(n, n XOR k), where T(n,k) is sequence A001477 considered as a two-dimensional table, and XOR is bitwise-xor (A003987).

Original entry on oeis.org

2, 11, 13, 7, 5, 8, 22, 8, 7, 26, 16, 38, 9, 42, 19, 37, 47, 58, 62, 52, 43, 29, 23, 48, 14, 51, 25, 34, 56, 30, 39, 19, 16, 41, 33, 64, 46, 80, 31, 25, 20, 23, 32, 88, 53, 79, 93, 108, 32, 41, 39, 31, 116, 102, 89, 67, 57, 94, 140, 33, 27, 30, 148, 101, 63, 76, 106, 68, 81, 157, 176, 34, 29, 184, 166, 87, 75, 118, 92, 138, 69, 175, 158, 216, 35, 224, 165, 185, 74, 150, 103

Offset: 1

Antti Karttunen, May 03 2017

			The top left 1 .. 12 x 1 .. 12 corner of the array:
    2,  11,   7,  22,  16,  37,  29,  56,  46,  79,  67, 106
   13,   5,   8,  38,  47,  23,  30,  80,  93,  57,  68, 138
    8,   7,   9,  58,  48,  39,  31, 108,  94,  81,  69, 174
   26,  42,  62,  14,  19,  25,  32, 140, 157, 175, 194,  82
   19,  52,  51,  16,  20,  41,  33, 176, 158, 215, 195, 110
   43,  25,  41,  23,  39,  27,  34, 216, 237, 177, 196, 142
   34,  33,  32,  31,  30,  29,  35, 260, 238, 217, 197, 178
   64,  88, 116, 148, 184, 224, 268,  44,  53,  63,  74,  86
   53, 102, 101, 166, 165, 246, 245,  46,  54,  87,  75, 114
   89,  63,  87, 185, 225, 183, 223,  57,  81,  65,  76, 146
   76,  75,  74, 205, 204, 203, 202,  69,  68,  67,  77, 182
  118, 150, 186,  86, 114, 146, 182,  82, 110, 142, 178,  90

Antti Karttunen, Table of n, a(n) for n = 1..10585; the first 145 antidiagonals of array

Array A286151 without its topmost row and leftmost column.

Cf. A003987, A091255, A286155.

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 + 1], {n, 20}, {k, n}] // Flatten (* Indranil Ghosh, May 21 2017 *)

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(1, 21): print([A(k, n - k + 1) for k in range(1, n + 1)]) # Indranil Ghosh, May 21 2017

(define (A286153 n) (A286151bi (A002260 n) (A004736 n))) ;; For A286151bi see A286151.

A(n,k) = A286151(n,k), for n >= 1, k >= 1.

If n > k, A(n,k) = T(A003987(n,k),k), otherwise A(n,k) = T(n,A003987(n,k)), where T(n,k) is sequence A001477 considered as a two-dimensional table, and XOR is bitwise-xor (A003987).

A286155 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).

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, May 03 2017

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.

			The top left 1 .. 12 x 1 .. 12 corner of the array:
  -1,   4,   2,  11,   7,  22,  16,  37,  29,  56,  46,  79
   6,  -2,   3,  23,  30,  12,  17,  57,  68,  38,  47, 107
   3,   2,  -3,  39,  31,  24,  18,  81,  69,  58,  48, 139
  15,  27,  43,  -4,  10,  14,  19, 109, 124, 140, 157,  59
  10,  35,  34,   7,  -5,  26,  20, 141, 125, 176, 158,  83
  28,  14,  26,  12,  24,  -6,  21, 177, 196, 142, 159, 111
  21,  20,  19,  18,  17,  16,  -7, 217, 197, 178, 160, 143
  45,  65,  89, 117, 149, 185, 225,  -8,  36,  44,  53,  63
  36,  77,  76, 133, 132, 205, 204,  29,  -9,  64,  54,  87
  66,  44,  64, 150, 186, 148, 184,  38,  58, -10,  55, 115
  55,  54,  53, 168, 167, 166, 165,  48,  47,  46, -11, 147
  91, 119, 151,  63,  87, 115, 147,  59,  83, 111, 143, -12

Antti Karttunen, Table of n, a(n) for n = 1..10585; the first 145 antidiagonals of array
MathWorld, Pairing Function

Cf. A003987, A091255.

Cf. also arrays A285732, A286151, A286153.

(define (A286155 n) (A286155bi (A002260 n) (A004736 n)))
(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).
(define (A000027bi row col) (* (/ 1 2) (+ (expt (+ row col) 2) (- row) (- (* 3 col)) 2)))

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.

cp's OEIS Frontend

A286108 Square array read by antidiagonals: A(n,k) = T(2*(n AND k), n XOR k), where T(n,k) is sequence A001477 considered as a two-dimensional table, AND is bitwise-and (A004198) and XOR is bitwise-xor (A003987).

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A286109 Square array read by antidiagonals: A(n,k) = T(n XOR k, 2*(n AND k)), where T(n,k) is sequence A001477 considered as a two-dimensional table, AND is bitwise-and (A004198) and XOR is bitwise-xor (A003987).

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A286145 Square 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).

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A286147 Square array read by antidiagonals: A(n,k) = T(n XOR k, n), where T(n,k) is sequence A001477 considered as a two-dimensional table, and XOR is bitwise-xor (A003987).

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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).

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A286153 Square array read by descending antidiagonals A(1,1), A(1,2), A(2,1), ...: If n > k, A(n,k) = T(n XOR k, k), and otherwise A(n,k) = T(n, n XOR k), where T(n,k) is sequence A001477 considered as a two-dimensional table, and XOR is bitwise-xor (A003987).

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A286155 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).

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