A263256 -id:A263256 - cp's OEIS frontend

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

Antti Karttunen, Nov 07 2015

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.

			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
  ...

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.

A263265 Irregular triangle T(n,k), n >= 0, k = 1 .. A262507(n), read by rows, where each row n lists in ascending order all integers x for which A155043(x) = n.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 5, 8, 9, 10, 12, 7, 11, 14, 18, 13, 15, 16, 20, 22, 17, 24, 25, 26, 28, 30, 19, 21, 32, 34, 23, 38, 40, 42, 27, 44, 46, 48, 29, 36, 49, 50, 52, 54, 56, 60, 31, 33, 58, 72, 35, 62, 66, 84, 37, 39, 68, 70, 96, 41, 45, 74, 76, 78, 80, 104, 108, 43, 47, 81, 82, 88, 90, 120, 51, 83, 85, 86, 94, 128, 132, 53, 55, 87, 92, 102, 136, 140

Offset: 0

Antti Karttunen, Nov 24 2015

			Rows 0 - 8 of the triangle:
0;
1, 2;
3, 4, 6;
5, 8, 9, 10, 12;
7, 11, 14, 18;
13, 15, 16, 20, 22;
17, 24, 25, 26, 28, 30;
19, 21, 32, 34;
23, 38, 40, 42;
Row n contains A262507(n) terms, the first of which is A261089(n) and the last of which is A262503(n). For all terms on row n, A155043(n) = n.

Inverse: A263266.
Cf. A261089 (left edge), A262503 (right edge), A262507 (number of terms on each row).
Cf. A263279 (gives the positions of terms of A259934 on each row), A263280 (and their distance from the right edge).
Cf. A155043, A263259, A263270.
Cf. also permutations A263267 & A263268 and A263255 & A263256.
Differs from A263267 for the first time at n=31, where a(31) = 38, while A263267(31) = 40.

Other identities. For all n >= 0:

A155043(a(n)) = A263270(n).

cp's OEIS Frontend

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.

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