A286153 - OEIS

%I #12 Dec 07 2019 12:18:29

%S 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,

%T 51,25,34,56,30,39,19,16,41,33,64,46,80,31,25,20,23,32,88,53,79,93,

%U 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

%N 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).

%H Antti Karttunen, <a href="/A286153/b286153.txt">Table of n, a(n) for n = 1..10585; the first 145 antidiagonals of array</a>

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

%F 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).

%e The top left 1 .. 12 x 1 .. 12 corner of the array:

%e     2,  11,   7,  22,  16,  37,  29,  56,  46,  79,  67, 106

%e    13,   5,   8,  38,  47,  23,  30,  80,  93,  57,  68, 138

%e     8,   7,   9,  58,  48,  39,  31, 108,  94,  81,  69, 174

%e    26,  42,  62,  14,  19,  25,  32, 140, 157, 175, 194,  82

%e    19,  52,  51,  16,  20,  41,  33, 176, 158, 215, 195, 110

%e    43,  25,  41,  23,  39,  27,  34, 216, 237, 177, 196, 142

%e    34,  33,  32,  31,  30,  29,  35, 260, 238, 217, 197, 178

%e    64,  88, 116, 148, 184, 224, 268,  44,  53,  63,  74,  86

%e    53, 102, 101, 166, 165, 246, 245,  46,  54,  87,  75, 114

%e    89,  63,  87, 185, 225, 183, 223,  57,  81,  65,  76, 146

%e    76,  75,  74, 205, 204, 203, 202,  69,  68,  67,  77, 182

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

%t 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 *)

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

%o (Python)

%o def T(a, b): return ((a + b)**2 + 3*a + b)/2

%o def A(n, k): return T(n^k, k) if n>k else T(n, n^k)

%o for n in range(1, 21): print [A(k, n - k + 1) for k in range(1, n + 1)] # _Indranil Ghosh_, May 21 2017

%Y Array A286151 without its topmost row and leftmost column.

%Y Cf. A003987, A091255, A286155.

%K nonn,tabl

%O 1,1

%A _Antti Karttunen_, May 03 2017