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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. 13

%I

%S 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 21,23,34,38,44,16,72,84,93,27,42,49,48,20,87,89,95,97,29,46,52,81,40,

%U 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 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 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 Antti Karttunen, <a href="/A263255/b263255.txt">Table of n, a(n) for n = 0..10439; the first 144 antidiagonals of array</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%e Top left corner of the array:

%e 0, 2, 6, 12, 18, 22, 30, 34, 42, 46, 54, 58, 62, 70

%e 1, 9, 10, 25, 26, 28, 38, 49, 52, 66, 68, 74, 76, 80

%e 3, 4, 11, 14, 32, 44, 48, 81, 86, 88, 116, 130, 135, 175

%e 5, 8, 13, 15, 16, 20, 40, 50, 56, 60, 83, 85, 92, 134

%e 7, 17, 24, 72, 87, 98, 139, 141, 142, 150, 202, 208, 225, 228

%e 19, 21, 84, 89, 91, 143, 145, 146, 147, 148, 206, 220, 227, 301

%e 23, 93, 95, 96, 100, 149, 153, 154, 160, 212, 229, 240, 305, 356

%e 27, 97, 99, 104, 108, 151, 158, 224, 248, 307, 309, 379, 381, 385

%e 29, 36, 101, 105, 120, 155, 164, 232, 260, 264, 311, 324, 383, 387

%e 31, 33, 103, 107, 128, 132, 157, 159, 276, 280, 313, 389, 391, 453

%e 35, 109, 111, 136, 140, 161, 165, 393, 395, 399, 461, 465, 532, 540

%e 37, 39, 113, 115, 117, 163, 167, 171, 397, 401, 403, 405, 463, 467

%e 41, 45, 119, 173, 407, 471, 473, 475, 568, 571, 572, 573, 575, 659

%e 43, 47, 123, 177, 409, 411, 477, 483, 484, 577, 578, 579, 580, 585

%e 51, 179, 413, 415, 479, 481, 495, 581, 583, 587, 589, 594, 671, 676

%e 53, 55, 181, 183, 417, 485, 591, 595, 602, 612, 673, 681, 877, 879

%e 57, 185, 187, 189, 419, 423, 487, 489, 593, 610, 683, 685, 693, 881

%e 59, 63, 64, 191, 195, 196, 421, 425, 427, 491, 493, 597, 614, 618

%e 61, 193, 197, 429, 435, 497, 599, 603, 622, 691, 705, 893, 895, 897

%e 65, 199, 201, 431, 499, 501, 601, 605, 626, 628, 695, 711, 899, 901

%e ...

%o (Scheme, with _Antti Karttunen_'s IntSeq-library)

%o (define (A263255 n) (A263255bi (A002262 n) (+ 1 (A025581 n))))

%o (define (A263255bi row col) ((rowfun-for-A263255 row) col))

%o (definec (rowfun-for-A263255 n) (if (zero? n) (COMPOSE A259934 -1+) (MATCHING-POS 1 0 (lambda (k) (= n (A263254 k))))))

%Y Transpose: A263256.

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

%Y Column 0: A263257.

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

%Y Cf. also array A262898.

%K nonn,tabl

%O 0,2

%A _Antti Karttunen_, Nov 07 2015

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Last modified October 22 08:00 EDT 2019. Contains 328315 sequences. (Running on oeis4.)