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A255555
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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)).
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9
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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FORMULA
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A(1,1) = 1, A(row,1) = A055938(row-1), and for col > 1, A(row,col) = A005187(1+A(row,col-1)).
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EXAMPLE
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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
...
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PROG
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(Scheme)
(define (A255555bi row col) (if (= 1 col) (if (= 1 row) 1 (A055938 (- row 1))) (A005187 (+ 1 (A255555bi row (- col 1))))))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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