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

Author

Antti Karttunen, Apr 14 2015

Keywords

• nonn
• tabl

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.

Examples

			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
  ...
		

Links

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

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).

Programs

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)))))

Formula

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