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A255557 Square array A(row,col): A(1,1) = 1, A(1,col) = A055938(col-1), and for row > 1: A(row,col) = A005187(1+A(row-1,col)). 9
1, 2, 3, 5, 4, 7, 6, 10, 8, 15, 9, 11, 19, 16, 31, 12, 18, 22, 38, 32, 63, 13, 23, 35, 42, 74, 64, 127, 14, 25, 46, 70, 82, 146, 128, 255, 17, 26, 49, 89, 138, 162, 290, 256, 511, 20, 34, 50, 97, 176, 274, 322, 578, 512, 1023, 21, 39, 67, 98, 193, 350, 546, 642, 1154, 1024, 2047, 24, 41, 78, 134, 194, 385, 695, 1090, 1282, 2306, 2048, 4095 (list; table; graph; refs; listen; history; text; internal format)
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.

This is transpose of array A255555, see comments and links given there.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of array

Index entries for sequences that are permutations of the natural numbers

FORMULA

A(row,col): A(1,1) = 1, and for the rest of topmost row: A(1,col) = A055938(col-1), and for any row > 1: A(row,col) = A005187(1+A(row-1,col)).

EXAMPLE

The top left corner of the array:

     1,    2,    5,    6,    9,   12,   13,   14,   17,   20,    21,    24

     3,    4,   10,   11,   18,   23,   25,   26,   34,   39,    41,    47

     7,    8,   19,   22,   35,   46,   49,   50,   67,   78,    81,    94

    15,   16,   38,   42,   70,   89,   97,   98,  134,  153,   161,   184

    31,   32,   74,   82,  138,  176,  193,  194,  266,  304,   321,   365

    63,   64,  146,  162,  274,  350,  385,  386,  530,  606,   641,   726

   127,  128,  290,  322,  546,  695,  769,  770, 1058, 1207,  1281,  1447

   255,  256,  578,  642, 1090, 1387, 1537, 1538, 2114, 2411,  2561,  2891

   511,  512, 1154, 1282, 2178, 2770, 3073, 3074, 4226, 4818,  5121,  5778

  1023, 1024, 2306, 2562, 4354, 5535, 6145, 6146, 8450, 9631, 10241, 11551

  ...

PROG

(Scheme)

(define (A255557 n) (A255555bi (A004736 n) (A002260 n)))

(define (A255555bi row col) (if (= 1 col) (if (= 1 row) 1 (A055938 (- row 1))) (A005187 (+ 1 (A255555bi row (- col 1))))))

CROSSREFS

Inverse permutation: A255558.

Transpose: A255555.

Column 1: A000225.

Cf. A005187, A055938.

Cf. A255559 (row index), A255560 (column index).

Cf. also A254107, A256997 (variants).

Sequence in context: A265888 A095721 A072061 * A261102 A101212 A232641

Adjacent sequences:  A255554 A255555 A255556 * A255558 A255559 A255560

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, Apr 13 2015

STATUS

approved

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Last modified February 22 10:25 EST 2019. Contains 320391 sequences. (Running on oeis4.)