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A256997 Square array A(row,col) read by antidiagonals: A(1,col) = A055938(col), and for row > 1, A(row,col) = A005187(A(row-1,col)). 13
2, 5, 3, 6, 8, 4, 9, 10, 15, 7, 12, 16, 18, 26, 11, 13, 22, 31, 34, 49, 19, 14, 23, 41, 57, 66, 95, 35, 17, 25, 42, 79, 110, 130, 184, 67, 20, 32, 47, 81, 153, 215, 258, 364, 131, 21, 38, 63, 89, 159, 302, 424, 514, 723, 259, 24, 39, 73, 120, 174, 312, 599, 844, 1026, 1440, 515, 27, 46, 74, 143, 236, 343, 620, 1192, 1683, 2050, 2876, 1027 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,1

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 A256995.

If we assume that a(1) = 1 (but which is not explicitly included here because outside of the array proper), then A256998 gives the inverse permutation.

LINKS

Antti Karttunen, Table of n, a(n) for n = 2..10441; the first 144 antidiagonals of square array

FORMULA

A(1,col) = A055938(col), and for row > 1, A(row,col) = A005187(A(row-1,col)).

EXAMPLE

The top left corner of the array:

    2,    5,    6,    9,   12,   13,   14,   17,   20,   21,    24,    27

    3,    8,   10,   16,   22,   23,   25,   32,   38,   39,    46,    50

    4,   15,   18,   31,   41,   42,   47,   63,   73,   74,    88,    97

    7,   26,   34,   57,   79,   81,   89,  120,  143,  145,   173,   191

   11,   49,   66,  110,  153,  159,  174,  236,  281,  287,   341,   375

   19,   95,  130,  215,  302,  312,  343,  467,  558,  568,   677,   743

   35,  184,  258,  424,  599,  620,  680,  928, 1111, 1132,  1349,  1479

   67,  364,  514,  844, 1192, 1235, 1356, 1852, 2216, 2259,  2693,  2951

  131,  723, 1026, 1683, 2380, 2464, 2707, 3697, 4428, 4512,  5381,  5895

  259, 1440, 2050, 3360, 4755, 4924, 5408, 7387, 8851, 9020, 10757, 11783

  ...

PROG

(Scheme)

(define (A256997 n) (if (<= n 1) n (A256997bi (A002260 (- n 1)) (A004736 (- n 1)))))

(define (A256997bi row col) (if (= 1 row) (A055938 col) (A005187 (A256997bi (- row 1) col))))

CROSSREFS

Cf. A005187, A055938 (row 1), A256994 (column 1), A256989 (row index), A256990 (column index).

Inverse: A256998.

Transpose: A256995.

Cf. also A254107, A255557 (variants), A246278 (another thematically similar construction).

Sequence in context: A024871 A222072 A246007 * A335499 A239970 A111202

Adjacent sequences:  A256994 A256995 A256996 * A256998 A256999 A257000

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, Apr 14 2015

STATUS

approved

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Last modified September 30 23:44 EDT 2020. Contains 337440 sequences. (Running on oeis4.)