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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.

%I A263255 #15 Nov 09 2015 16:07:37
%S A263255 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,
%T A263255 21,23,34,38,44,16,72,84,93,27,42,49,48,20,87,89,95,97,29,46,52,81,40,
%U A263255 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
%N 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.
%C A263255 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.
%H A263255 Antti Karttunen, <a href="/A263255/b263255.txt">Table of n, a(n) for n = 0..10439; the first 144 antidiagonals of array</a>
%H A263255 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A263255 Top left corner of the array:
%e A263255    0,   2,   6,  12,  18,  22,  30,  34,  42,  46,  54,  58,  62,  70
%e A263255    1,   9,  10,  25,  26,  28,  38,  49,  52,  66,  68,  74,  76,  80
%e A263255    3,   4,  11,  14,  32,  44,  48,  81,  86,  88, 116, 130, 135, 175
%e A263255    5,   8,  13,  15,  16,  20,  40,  50,  56,  60,  83,  85,  92, 134
%e A263255    7,  17,  24,  72,  87,  98, 139, 141, 142, 150, 202, 208, 225, 228
%e A263255   19,  21,  84,  89,  91, 143, 145, 146, 147, 148, 206, 220, 227, 301
%e A263255   23,  93,  95,  96, 100, 149, 153, 154, 160, 212, 229, 240, 305, 356
%e A263255   27,  97,  99, 104, 108, 151, 158, 224, 248, 307, 309, 379, 381, 385
%e A263255   29,  36, 101, 105, 120, 155, 164, 232, 260, 264, 311, 324, 383, 387
%e A263255   31,  33, 103, 107, 128, 132, 157, 159, 276, 280, 313, 389, 391, 453
%e A263255   35, 109, 111, 136, 140, 161, 165, 393, 395, 399, 461, 465, 532, 540
%e A263255   37,  39, 113, 115, 117, 163, 167, 171, 397, 401, 403, 405, 463, 467
%e A263255   41,  45, 119, 173, 407, 471, 473, 475, 568, 571, 572, 573, 575, 659
%e A263255   43,  47, 123, 177, 409, 411, 477, 483, 484, 577, 578, 579, 580, 585
%e A263255   51, 179, 413, 415, 479, 481, 495, 581, 583, 587, 589, 594, 671, 676
%e A263255   53,  55, 181, 183, 417, 485, 591, 595, 602, 612, 673, 681, 877, 879
%e A263255   57, 185, 187, 189, 419, 423, 487, 489, 593, 610, 683, 685, 693, 881
%e A263255   59,  63,  64, 191, 195, 196, 421, 425, 427, 491, 493, 597, 614, 618
%e A263255   61, 193, 197, 429, 435, 497, 599, 603, 622, 691, 705, 893, 895, 897
%e A263255   65, 199, 201, 431, 499, 501, 601, 605, 626, 628, 695, 711, 899, 901
%e A263255   ...
%o A263255 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A263255 (define (A263255 n) (A263255bi (A002262 n) (+ 1 (A025581 n))))
%o A263255 (define (A263255bi row col) ((rowfun-for-A263255 row) col))
%o A263255 (definec (rowfun-for-A263255 n) (if (zero? n) (COMPOSE A259934 -1+) (MATCHING-POS 1 0 (lambda (k) (= n (A263254 k))))))
%Y A263255 Transpose: A263256.
%Y A263255 Row 0: A259934, Row 1: A263261, Row 2: A263262, Row 3: A263263, Row 4: A263264.
%Y A263255 Column 0: A263257.
%Y A263255 Cf. A263254 (row index, zero-based), A263275 (row index, one-based), A263274 (column index, one-based).
%Y A263255 Cf. also array A262898.
%K A263255 nonn,tabl
%O A263255 0,2
%A A263255 _Antti Karttunen_, Nov 07 2015