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).

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

Author

Antti Karttunen, May 03 2017

Keywords

• nonn
• tabl

Examples

			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
		

Links

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

Crossrefs

Array A286151 without its topmost row and leftmost column.

Cf. A003987, A091255, A286155.

Programs

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

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

Scheme

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

Formula

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).