cp's OEIS Frontend

A268830 Square array A(r,c): A(0,c) = c, A(r,0) = 0, A(r>=1,c>=1) = 1+A(r-1,A268718(c)-1) = 1 + A(r-1, A003188(A006068(c)-1)), read by descending antidiagonals.

%I A268830 #23 Mar 28 2021 07:00:55
%S A268830 0,1,0,2,1,0,3,4,1,0,4,2,3,1,0,5,6,2,3,1,0,6,8,9,2,3,1,0,7,3,8,9,2,3,
%T A268830 1,0,8,7,5,5,6,2,3,1,0,9,10,4,4,7,8,2,3,1,0,10,12,13,6,4,6,7,2,3,1,0,
%U A268830 11,15,12,13,5,4,6,7,2,3,1,0,12,11,17,17,18,5,4,6,7,2,3,1,0,13,5,16,16,19,20,5,4,6,7,2,3,1,0,14,13,7,18,16,18,19,5,4,6,7,2,3,1,0
%N A268830 Square array A(r,c): A(0,c) = c, A(r,0) = 0, A(r>=1,c>=1) = 1+A(r-1,A268718(c)-1) = 1 + A(r-1, A003188(A006068(c)-1)), read by descending antidiagonals.
%H A268830 Antti Karttunen, <a href="/A268830/b268830.txt">Table of n, a(n) for n = 0..32895; the first 256 antidiagonals of array</a>
%e A268830 The top left [0 .. 16] x [0 .. 19] section of the array:
%e A268830 0, 1, 2, 3, 4, 5, 6, 7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
%e A268830 0, 1, 4, 2, 6, 8, 3, 7, 10, 12, 15, 11,  5, 13, 16, 14, 18, 20, 23, 19
%e A268830 0, 1, 3, 2, 9, 8, 5, 4, 13, 12, 17, 16,  7,  6, 15, 14, 21, 20, 25, 24
%e A268830 0, 1, 3, 2, 9, 5, 4, 6, 13, 17, 16, 18, 10,  8, 15,  7, 21, 25, 24, 26
%e A268830 0, 1, 3, 2, 6, 7, 4, 5, 18, 19, 16, 17, 10, 11,  8,  9, 26, 27, 24, 25
%e A268830 0, 1, 3, 2, 8, 6, 4, 5, 20, 18,  9, 17,  7, 11, 10, 12, 28, 26, 33, 25
%e A268830 0, 1, 3, 2, 7, 6, 4, 5, 19, 18, 11, 10,  9,  8, 13, 12, 27, 26, 35, 34
%e A268830 0, 1, 3, 2, 7, 6, 4, 5, 19, 11, 14, 12,  8, 10, 13,  9, 27, 35, 38, 36
%e A268830 0, 1, 3, 2, 7, 6, 4, 5, 12, 13, 14, 15,  8,  9, 10, 11, 36, 37, 38, 39
%e A268830 0, 1, 3, 2, 7, 6, 4, 5, 14, 16, 11, 15,  8,  9, 12, 10, 38, 40, 35, 39
%e A268830 0, 1, 3, 2, 7, 6, 4, 5, 17, 16, 13, 12,  8,  9, 11, 10, 41, 40, 37, 36
%e A268830 0, 1, 3, 2, 7, 6, 4, 5, 17, 13, 12, 14,  8,  9, 11, 10, 41, 37, 36, 38
%e A268830 0, 1, 3, 2, 7, 6, 4, 5, 14, 15, 12, 13,  8,  9, 11, 10, 38, 39, 36, 37
%e A268830 0, 1, 3, 2, 7, 6, 4, 5, 16, 14, 12, 13,  8,  9, 11, 10, 40, 38, 21, 37
%e A268830 0, 1, 3, 2, 7, 6, 4, 5, 15, 14, 12, 13,  8,  9, 11, 10, 39, 38, 23, 22
%e A268830 0, 1, 3, 2, 7, 6, 4, 5, 15, 14, 12, 13,  8,  9, 11, 10, 39, 23, 26, 24
%e A268830 0, 1, 3, 2, 7, 6, 4, 5, 15, 14, 12, 13,  8,  9, 11, 10, 24, 25, 26, 27
%o A268830 (Scheme)
%o A268830 (define (A268830 n) (A268830bi (A002262 n) (A025581 n))) ;; o=0: Square array of shifted powers of A268718.
%o A268830 (define (A268830bi row col) (cond ((zero? row) col) ((zero? col) 0) (else (+ 1 (A268830bi (- row 1) (- (A268718 col) 1))))))
%o A268830 (define (A268830bi row col) (cond ((zero? row) col) ((zero? col) 0) (else (+ 1 (A268830bi (- row 1) (A003188 (+ -1 (A006068 col))))))))
%o A268830 (Python)
%o A268830 def a003188(n): return n^(n>>1)
%o A268830 def a006068(n):
%o A268830     s=1
%o A268830     while True:
%o A268830         ns=n>>s
%o A268830         if ns==0: break
%o A268830         n=n^ns
%o A268830         s<<=1
%o A268830     return n
%o A268830 def a278618(n): return 0 if n==0 else 1 + a003188(a006068(n) - 1)
%o A268830 def A(r, c): return c if r==0 else 0 if c==0 else 1 + A(r - 1, a278618(c) - 1)
%o A268830 for r in range(21): print([A(c, r - c) for c in range(r + 1)]) # _Indranil Ghosh_, Jun 07 2017
%Y A268830 Cf. A003188, A006068.
%Y A268830 Inverses of these permutations can be found in table A268820.
%Y A268830 Row 0: A001477, Row 1: A268718, Row 2: A268822, Row 3: A268824, Row 4: A268826, Row 5: A268828, Row 6: A268832, Row 7: A268934.
%Y A268830 Rows converge towards A006068.
%K A268830 nonn,tabl
%O A268830 0,4
%A A268830 _Antti Karttunen_, Feb 14 2016