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

0,4

Links

Antti Karttunen, Table of n, a(n) for n = 0..32895; the first 256 antidiagonals of array

Example

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

Prog

(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))))))))
(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

Crossrefs

Cf. A003188, A006068.

Inverses of these permutations can be found in table A268820.

Row 0: A001477, Row 1: A268718, Row 2: A268822, Row 3: A268824, Row 4: A268826, Row 5: A268828, Row 6: A268832, Row 7: A268934.

Rows converge towards A006068.

Sequence in context: A357368 A193401 A220399 * A095884 A342240 A128908

Adjacent sequences: A268827 A268828 A268829 * A268831 A268832 A268833

Keyword

nonn,tabl

Author

Antti Karttunen, Feb 14 2016

Status

approved