A256995 Square array A(row,col) read by antidiagonals: A(row,1) = A055938(row), and for col > 1, A(row,col) = A005187(A(row,col-1)).

2, 3, 5, 4, 8, 6, 7, 15, 10, 9, 11, 26, 18, 16, 12, 19, 49, 34, 31, 22, 13, 35, 95, 66, 57, 41, 23, 14, 67, 184, 130, 110, 79, 42, 25, 17, 131, 364, 258, 215, 153, 81, 47, 32, 20, 259, 723, 514, 424, 302, 159, 89, 63, 38, 21, 515, 1440, 1026, 844, 599, 312, 174, 120, 73, 39, 24, 1027, 2876, 2050, 1683, 1192, 620, 343, 236, 143, 74, 46, 27

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 A256997.

If we assume that a(1) = 1 (but which is not explicitly included here because outside of the array proper), then A256996 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(row,1) = A055938(row), and for col > 1, A(row,col) = A005187(A(row,col-1)).

Example

The top left corner of the array:
   2,  3,  4,   7,  11,  19,   35,   67,  131,  259,   515,  1027
   5,  8, 15,  26,  49,  95,  184,  364,  723, 1440,  2876,  5745
   6, 10, 18,  34,  66, 130,  258,  514, 1026, 2050,  4098,  8194
   9, 16, 31,  57, 110, 215,  424,  844, 1683, 3360,  6716, 13425
  12, 22, 41,  79, 153, 302,  599, 1192, 2380, 4755,  9504, 19004
  13, 23, 42,  81, 159, 312,  620, 1235, 2464, 4924,  9841, 19675
  14, 25, 47,  89, 174, 343,  680, 1356, 2707, 5408, 10812, 21617
  17, 32, 63, 120, 236, 467,  928, 1852, 3697, 7387, 14765, 29521
  20, 38, 73, 143, 281, 558, 1111, 2216, 4428, 8851, 17696, 35388
  21, 39, 74, 145, 287, 568, 1132, 2259, 4512, 9020, 18033, 36059
  ...

Prog

(Scheme)
(define (A256995 n) (if (<= n 1) n (A256995bi (A002260 (- n 1)) (A004736 (- n 1)))))
(define (A256995bi row col) (if (= 1 col) (A055938 row) (A005187 (A256995bi row (- col 1)))))

Crossrefs

Inverse permutation: A256996.

Transpose: A256997.

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

Cf. also A254105, A255555 (variants), A114537, A246279 (other thematically similar constructions).

Sequence in context: A347423 A255234 A364225 * A249129 A065561 A245708

Adjacent sequences: A256992 A256993 A256994 * A256996 A256997 A256998

Keyword

nonn,tabl

Author

Antti Karttunen, Apr 14 2015

Status

approved