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.

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

0,3

Links

Antti Karttunen, Table of n, a(n) for n = 0..125752; rows 0 .. 10001 of the irregular table

Index entries for sequences that are permutations of the natural numbers

Formula

Other identities. For all n >= 0:

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

Example

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.

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(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))))))))

Crossrefs

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.

Sequence in context: A094138 A116538 A084287 * A263267 A257471 A369136

Adjacent sequences: A263262 A263263 A263264 * A263266 A263267 A263268

Keyword

nonn,tabf

Author

Antti Karttunen, Nov 24 2015

Status

approved