A255555 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)).

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

Offset: 1

Author

Antti Karttunen, Apr 13 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.

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

Examples

			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
  ...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of array
• Clark Kimberling, Interspersions and Dispersions.
• Clark Kimberling, Interspersions and Dispersions, Proceedings of the American Mathematical Society, 117 (1993) 313-321.
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse permutation: A255556.

Transpose: A255557.

Row 1: A000225.

Cf. A005187, A055938.

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

Cf. also A254105, A256995 (variants), A233275-A233278.

Programs

Scheme

(define (A255555 n) (A255555bi (A002260 n) (A004736 n)))
(define (A255555bi row col) (if (= 1 col) (if (= 1 row) 1 (A055938 (- row 1))) (A005187 (+ 1 (A255555bi row (- col 1))))))

Formula

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