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 A268834 Transpose of array A268833. 3
 0, 1, 0, 2, 1, 0, 1, 2, 1, 0, 2, 3, 2, 1, 0, 3, 2, 3, 2, 1, 0, 2, 1, 2, 1, 2, 1, 0, 1, 2, 3, 2, 3, 2, 1, 0, 2, 3, 4, 3, 2, 1, 2, 1, 0, 3, 2, 3, 4, 3, 2, 1, 2, 1, 0, 4, 3, 2, 3, 4, 3, 2, 3, 2, 1, 0, 3, 4, 1, 2, 3, 4, 3, 2, 3, 2, 1, 0, 2, 3, 2, 3, 2, 3, 2, 1, 2, 1, 2, 1, 0, 3, 2, 3, 2, 3, 2, 1, 2, 3, 2, 1, 2, 1, 0, 2, 1, 2, 1, 4, 3, 2, 3, 4, 3, 2, 3, 2, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS See comments in A268833. LINKS EXAMPLE The top left [0 .. 16] x [0 .. 16] section of the array:   0, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 3, 2, 1, 2   0, 1, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 2, 1, 2, 3, 2   0, 1, 2, 3, 2, 3, 4, 3, 2, 1, 2, 3, 2, 3, 4, 3, 2   0, 1, 2, 1, 2, 3, 4, 3, 2, 3, 2, 1, 2, 3, 4, 3, 2   0, 1, 2, 3, 2, 3, 4, 3, 2, 3, 4, 5, 4, 3, 4, 3, 2   0, 1, 2, 1, 2, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 3, 2   0, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 4, 5, 4, 3, 2   0, 1, 2, 3, 2, 1, 2, 3, 2, 3, 4, 5, 4, 3, 4, 3, 2   0, 1, 2, 3, 2, 3, 4, 3, 2, 3, 4, 5, 4, 3, 4, 3, 2   0, 1, 2, 1, 2, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 3, 2   0, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 4, 5, 4, 3, 2   0, 1, 2, 3, 2, 1, 2, 3, 2, 3, 4, 5, 4, 3, 4, 3, 2   0, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 3, 2, 1, 2   0, 1, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 2, 1, 2, 3, 2   0, 1, 2, 3, 2, 3, 4, 3, 2, 1, 2, 3, 2, 3, 4, 3, 2   0, 1, 2, 1, 2, 3, 4, 3, 2, 3, 2, 1, 2, 3, 4, 3, 2   0, 1, 2, 3, 2, 3, 4, 3, 2, 3, 4, 5, 4, 3, 4, 3, 2 MATHEMATICA A101080[n_, k_]:= DigitCount[BitXor[n, k], 2, 1]; A003188[n_]:=BitXor[n, Floor[n/2]]; A006068[n_]:=If[n<2, n, Block[{m=A006068[Floor[n/2]]}, 2m + Mod[Mod[n, 2] + Mod[m, 2], 2]]]; a[r_, 0]:= 0; a[0, c_]:=c; a[r_, c_]:= A003188[1 + A006068[a[r - 1, c - 1]]]; A[r_, c_]:=A101080[c, a[r, r + c]]; Table[A[r - c, c], {r, 0, 20}, {c, 0, r}] // Flatten (* Indranil Ghosh, Apr 02 2017 *) PROG (Scheme) (define (A268834 n) (A268833bi (A025581 n) (A002262 n))) ;; Code for A268833bi given in A268833. (PARI) b(n) = if(n<1, 0, b(n\2) + n%2); A101080(n, k) = b(bitxor(n, k)); A003188(n) = bitxor(n, n\2); A006068(n) = if(n<2, n, {my(m = A006068(n\2)); 2*m + (n%2 + m%2)%2}); A268820(r, c) = if(r==0, c, if(c==0, 0, A003188(1 + A006068(A268820(r - 1, c - 1))))); A(r, c) = A101080(c, A268820(r, r + c)); for(r=0, 20, for(c=0, r, print1(A(r - c, c), ", "); ); print(); ) \\ Indranil Ghosh, Apr 02 2017 (Python) def A101080(n, k): return bin(n^k)[2:].count("1") def A003188(n): return n^(n/2) def A006068(n): ....if n<2: return n ....else: ........m=A006068(n/2) ........return 2*m + (n%2 + m%2)%2 def A268820(r, c): return c if r<1 else 0 if c<1 else A003188(1 + A006068(A268820(r - 1, c - 1))) def a(r, c): return A101080(c, A268820(r, r + c)) for r in range(0, 21): ....print [a(r - c, c) for c in range(0, r + 1)] # Indranil Ghosh, Apr 02 2017 CROSSREFS Transpose of A268833. Sequence in context: A025870 A104276 A216191 * A285914 A096875 A194514 Adjacent sequences:  A268831 A268832 A268833 * A268835 A268836 A268837 KEYWORD nonn,tabl AUTHOR Antti Karttunen, Feb 15 2016 STATUS approved

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Last modified August 3 07:58 EDT 2021. Contains 346435 sequences. (Running on oeis4.)