A263255 Square array A(r,c), where each row r lists all numbers that are r edges distant from the infinite trunk (A259934) of the tree defined by edge-relation A049820(child) = parent.

0, 2, 1, 6, 9, 3, 12, 10, 4, 5, 18, 25, 11, 8, 7, 22, 26, 14, 13, 17, 19, 30, 28, 32, 15, 24, 21, 23, 34, 38, 44, 16, 72, 84, 93, 27, 42, 49, 48, 20, 87, 89, 95, 97, 29, 46, 52, 81, 40, 98, 91, 96, 99, 36, 31, 54, 66, 86, 50, 139, 143, 100, 104, 101, 33, 35, 58, 68, 88, 56, 141, 145, 149, 108, 105, 103, 109, 37

Offset: 0

Author

Antti Karttunen, Nov 07 2015

Keywords

• nonn
• tabl

Comments

The array A(row>=0,col>=1) is read by downwards antidiagonals: A(0,1), A(0,2), A(1,1), A(0,3), A(1,2), A(2,1), A(0,4), A(1,3), A(2,2), A(3,1), etc.

Examples

			Top left corner of the array:
   0,   2,   6,  12,  18,  22,  30,  34,  42,  46,  54,  58,  62,  70
   1,   9,  10,  25,  26,  28,  38,  49,  52,  66,  68,  74,  76,  80
   3,   4,  11,  14,  32,  44,  48,  81,  86,  88, 116, 130, 135, 175
   5,   8,  13,  15,  16,  20,  40,  50,  56,  60,  83,  85,  92, 134
   7,  17,  24,  72,  87,  98, 139, 141, 142, 150, 202, 208, 225, 228
  19,  21,  84,  89,  91, 143, 145, 146, 147, 148, 206, 220, 227, 301
  23,  93,  95,  96, 100, 149, 153, 154, 160, 212, 229, 240, 305, 356
  27,  97,  99, 104, 108, 151, 158, 224, 248, 307, 309, 379, 381, 385
  29,  36, 101, 105, 120, 155, 164, 232, 260, 264, 311, 324, 383, 387
  31,  33, 103, 107, 128, 132, 157, 159, 276, 280, 313, 389, 391, 453
  35, 109, 111, 136, 140, 161, 165, 393, 395, 399, 461, 465, 532, 540
  37,  39, 113, 115, 117, 163, 167, 171, 397, 401, 403, 405, 463, 467
  41,  45, 119, 173, 407, 471, 473, 475, 568, 571, 572, 573, 575, 659
  43,  47, 123, 177, 409, 411, 477, 483, 484, 577, 578, 579, 580, 585
  51, 179, 413, 415, 479, 481, 495, 581, 583, 587, 589, 594, 671, 676
  53,  55, 181, 183, 417, 485, 591, 595, 602, 612, 673, 681, 877, 879
  57, 185, 187, 189, 419, 423, 487, 489, 593, 610, 683, 685, 693, 881
  59,  63,  64, 191, 195, 196, 421, 425, 427, 491, 493, 597, 614, 618
  61, 193, 197, 429, 435, 497, 599, 603, 622, 691, 705, 893, 895, 897
  65, 199, 201, 431, 499, 501, 601, 605, 626, 628, 695, 711, 899, 901
  ...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10439; the first 144 antidiagonals of array
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Transpose: A263256.

Row 0: A259934, Row 1: A263261, Row 2: A263262, Row 3: A263263, Row 4: A263264.

Column 0: A263257.

Cf. A263254 (row index, zero-based), A263275 (row index, one-based), A263274 (column index, one-based).

Cf. also array A262898.