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A255555
Square array A(row,col) read by downwards antidiagonals: A(1,1) = 1, A(row,1) = A055938(row-1), and for col > 1, A(row,col) = A005187(1+A(row,col-1)).
9
1, 3, 2, 7, 4, 5, 15, 8, 10, 6, 31, 16, 19, 11, 9, 63, 32, 38, 22, 18, 12, 127, 64, 74, 42, 35, 23, 13, 255, 128, 146, 82, 70, 46, 25, 14, 511, 256, 290, 162, 138, 89, 49, 26, 17, 1023, 512, 578, 322, 274, 176, 97, 50, 34, 20, 2047, 1024, 1154, 642, 546, 350, 193, 98, 67, 39, 21, 4095, 2048, 2306, 1282, 1090, 695, 385, 194, 134, 78, 41, 24
OFFSET
1,2
COMMENTS
The array is read by antidiagonals: A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.
Provided that I understand Kimberling's terminology correctly, this array is the dispersion of sequence b(n) = A005187(n+1), for n>=1: A005187[2..] = [3, 4, 7, 8, 10, 11, ...]. The left column is the complement of that sequence, which is {1} followed by A055938. - Antti Karttunen, Apr 17 2015
LINKS
FORMULA
A(1,1) = 1, A(row,1) = A055938(row-1), and for col > 1, A(row,col) = A005187(1+A(row,col-1)).
EXAMPLE
The top left corner of the array:
1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096
5, 10, 19, 38, 74, 146, 290, 578, 1154, 2306, 4610, 9218
6, 11, 22, 42, 82, 162, 322, 642, 1282, 2562, 5122, 10242
9, 18, 35, 70, 138, 274, 546, 1090, 2178, 4354, 8706, 17410
12, 23, 46, 89, 176, 350, 695, 1387, 2770, 5535, 11067, 22128
13, 25, 49, 97, 193, 385, 769, 1537, 3073, 6145, 12289, 24577
14, 26, 50, 98, 194, 386, 770, 1538, 3074, 6146, 12290, 24578
17, 34, 67, 134, 266, 530, 1058, 2114, 4226, 8450, 16898, 33794
20, 39, 78, 153, 304, 606, 1207, 2411, 4818, 9631, 19259, 38512
...
PROG
(Scheme)
(define (A255555 n) (A255555bi (A002260 n) (A004736 n)))
(define (A255555bi row col) (if (= 1 col) (if (= 1 row) 1 (A055938 (- row 1))) (A005187 (+ 1 (A255555bi row (- col 1))))))
CROSSREFS
Inverse permutation: A255556.
Transpose: A255557.
Row 1: A000225.
Cf. A255559 (column index), A255560 (row index).
Cf. also A254105, A256995 (variants), A233275-A233278.
Sequence in context: A370698 A303763 A303765 * A191664 A118319 A316385
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Apr 13 2015
STATUS
approved