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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).
5
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
1,1
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).
EXAMPLE
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
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 *)
PROG
(Scheme) (define (A286153 n) (A286151bi (A002260 n) (A004736 n))) ;; For A286151bi see A286151.
(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
CROSSREFS
Array A286151 without its topmost row and leftmost column.
Sequence in context: A037091 A289675 A127303 * A068972 A116437 A048867
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, May 03 2017
STATUS
approved