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.
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, 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, 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
Offset: 0
Examples
The top left [0 .. 16] x [0 .. 19] section of the array: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 0, 1, 4, 2, 6, 8, 3, 7, 10, 12, 15, 11, 5, 13, 16, 14, 18, 20, 23, 19 0, 1, 3, 2, 9, 8, 5, 4, 13, 12, 17, 16, 7, 6, 15, 14, 21, 20, 25, 24 0, 1, 3, 2, 9, 5, 4, 6, 13, 17, 16, 18, 10, 8, 15, 7, 21, 25, 24, 26 0, 1, 3, 2, 6, 7, 4, 5, 18, 19, 16, 17, 10, 11, 8, 9, 26, 27, 24, 25 0, 1, 3, 2, 8, 6, 4, 5, 20, 18, 9, 17, 7, 11, 10, 12, 28, 26, 33, 25 0, 1, 3, 2, 7, 6, 4, 5, 19, 18, 11, 10, 9, 8, 13, 12, 27, 26, 35, 34 0, 1, 3, 2, 7, 6, 4, 5, 19, 11, 14, 12, 8, 10, 13, 9, 27, 35, 38, 36 0, 1, 3, 2, 7, 6, 4, 5, 12, 13, 14, 15, 8, 9, 10, 11, 36, 37, 38, 39 0, 1, 3, 2, 7, 6, 4, 5, 14, 16, 11, 15, 8, 9, 12, 10, 38, 40, 35, 39 0, 1, 3, 2, 7, 6, 4, 5, 17, 16, 13, 12, 8, 9, 11, 10, 41, 40, 37, 36 0, 1, 3, 2, 7, 6, 4, 5, 17, 13, 12, 14, 8, 9, 11, 10, 41, 37, 36, 38 0, 1, 3, 2, 7, 6, 4, 5, 14, 15, 12, 13, 8, 9, 11, 10, 38, 39, 36, 37 0, 1, 3, 2, 7, 6, 4, 5, 16, 14, 12, 13, 8, 9, 11, 10, 40, 38, 21, 37 0, 1, 3, 2, 7, 6, 4, 5, 15, 14, 12, 13, 8, 9, 11, 10, 39, 38, 23, 22 0, 1, 3, 2, 7, 6, 4, 5, 15, 14, 12, 13, 8, 9, 11, 10, 39, 23, 26, 24 0, 1, 3, 2, 7, 6, 4, 5, 15, 14, 12, 13, 8, 9, 11, 10, 24, 25, 26, 27
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Crossrefs
Programs
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Python
def a003188(n): return n^(n>>1) def a006068(n): s=1 while True: ns=n>>s if ns==0: break n=n^ns s<<=1 return n def a278618(n): return 0 if n==0 else 1 + a003188(a006068(n) - 1) def A(r, c): return c if r==0 else 0 if c==0 else 1 + A(r - 1, a278618(c) - 1) for r in range(21): print([A(c, r - c) for c in range(r + 1)]) # Indranil Ghosh, Jun 07 2017 -
Scheme
(define (A268830 n) (A268830bi (A002262 n) (A025581 n))) ;; o=0: Square array of shifted powers of A268718. (define (A268830bi row col) (cond ((zero? row) col) ((zero? col) 0) (else (+ 1 (A268830bi (- row 1) (- (A268718 col) 1)))))) (define (A268830bi row col) (cond ((zero? row) col) ((zero? col) 0) (else (+ 1 (A268830bi (- row 1) (A003188 (+ -1 (A006068 col))))))))
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