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%I #22 Dec 03 2015 04:33:30
%S 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,
%T 19,21,32,34,23,38,40,42,27,44,46,48,29,36,49,50,52,54,56,60,31,33,58,
%U 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
%N 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.
%H Antti Karttunen, <a href="/A263265/b263265.txt">Table of n, a(n) for n = 0..125752; rows 0 .. 10001 of the irregular table</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F Other identities. For all n >= 0:
%F A155043(a(n)) = A263270(n).
%e Rows 0 - 8 of the triangle:
%e 0;
%e 1, 2;
%e 3, 4, 6;
%e 5, 8, 9, 10, 12;
%e 7, 11, 14, 18;
%e 13, 15, 16, 20, 22;
%e 17, 24, 25, 26, 28, 30;
%e 19, 21, 32, 34;
%e 23, 38, 40, 42;
%e 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.
%o (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o (defineperm1 (A263265 n) (cond ((zero? n) n) ((= 1 (- (A263270 n) (A263270 (- n 1)))) (A261089 (A263270 n))) (else (let ((p (A263265 (- n 1))) (d (A263270 n))) (let loop ((k (+ p 1))) (if (= (A155043 k) d) k (loop (+ k 1))))))))
%Y Inverse: A263266.
%Y Cf. A261089 (left edge), A262503 (right edge), A262507 (number of terms on each row).
%Y Cf. A263279 (gives the positions of terms of A259934 on each row), A263280 (and their distance from the right edge).
%Y Cf. A155043, A263259, A263270.
%Y Cf. also permutations A263267 & A263268 and A263255 & A263256.
%Y Differs from A263267 for the first time at n=31, where a(31) = 38, while A263267(31) = 40.
%K nonn,tabf
%O 0,3
%A _Antti Karttunen_, Nov 24 2015
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