A082853 -id:A082853 - cp's OEIS frontend

A082363 Permutation of natural numbers induced by the contraction of Catalan bijection signature-permutation A082355.

0, 1, 4, 2, 3, 10, 11, 12, 5, 6, 13, 9, 7, 8, 28, 29, 32, 30, 31, 33, 34, 35, 14, 15, 36, 18, 16, 17, 37, 38, 41, 24, 25, 39, 26, 19, 20, 40, 27, 23, 21, 22, 84, 85, 88, 86, 87, 94, 95, 96, 89, 90, 97, 93, 91, 92, 98, 99, 102, 100, 101, 103, 104, 105, 42, 43, 106, 46, 44, 45

Offset: 0

Antti Karttunen, Apr 17 2003

nonn

A. Karttunen, Table of n, a(n) for n = 0..1429
A. Karttunen, Gatomorphisms (with the complete Scheme source)
Index entries for signature-permutations induced by Catalan automorphisms

Compare to the plot of A070041.

Inverse of A082364. Cf. also A082361-A082362.

a(n) = A082853(A082355(A081291(n))).

A082364 Permutation of natural numbers induced by the contraction of Catalan bijection signature-permutation A082356.

Original entry on oeis.org

0, 1, 3, 4, 2, 8, 9, 12, 13, 11, 5, 6, 7, 10, 22, 23, 26, 27, 25, 35, 36, 40, 41, 39, 31, 32, 34, 38, 14, 15, 17, 18, 16, 19, 20, 21, 24, 28, 29, 33, 37, 30, 64, 65, 68, 69, 67, 77, 78, 82, 83, 81, 73, 74, 76, 80, 105, 106, 110, 111, 109, 124, 125, 130, 131, 129, 119, 120, 123

Offset: 0

Antti Karttunen, Apr 17 2003

nonn

A. Karttunen, Table of n, a(n) for n = 0..1429
A. Karttunen, Gatomorphisms (with the complete Scheme source)
Index entries for signature-permutations induced by Catalan automorphisms

Compare to the plot of A038776.

Inverse of A082363. Cf. also A082361-A082362.

a(n) = A082853(A082356(A081291(n))).

A082361 Permutation of natural numbers induced by the contraction of Catalan bijection signature-permutation A082351.

Original entry on oeis.org

0, 1, 4, 2, 3, 10, 11, 12, 5, 6, 13, 7, 8, 9, 28, 29, 30, 31, 32, 33, 34, 35, 14, 15, 36, 16, 17, 18, 37, 38, 39, 19, 20, 40, 21, 22, 23, 41, 24, 25, 26, 27, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 42, 43, 106, 44, 45, 46

Offset: 0

Antti Karttunen, Apr 17 2003

nonn

A. Karttunen, Gatomorphisms (with the complete Scheme source)
Index entries for signature-permutations induced by Catalan automorphisms

Inverse of A082362. Cf. also A082363-A082364.

a(n) = A082853(A082351(A081291(n))).

A082362 Permutation of natural numbers induced by the contraction of Catalan bijection signature-permutation A082352.

Original entry on oeis.org

0, 1, 3, 4, 2, 8, 9, 11, 12, 13, 5, 6, 7, 10, 22, 23, 25, 26, 27, 31, 32, 34, 35, 36, 38, 39, 40, 41, 14, 15, 16, 17, 18, 19, 20, 21, 24, 28, 29, 30, 33, 37, 64, 65, 67, 68, 69, 73, 74, 76, 77, 78, 80, 81, 82, 83, 92, 93, 95, 96, 97, 101, 102, 104, 105, 106, 108, 109, 110, 111

Offset: 0

Antti Karttunen, Apr 17 2003

nonn

A. Karttunen, Gatomorphisms (with the complete Scheme source)
Index entries for signature-permutations induced by Catalan automorphisms

Inverse of A082361. Cf. also A082363-A082364.

a(n) = A082853(A082352(A081291(n))).

A218601 After the first zero, integers from 0 to A213709(n)-1 followed by integers from 0 to A213709(n+1)-1, etc.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0

Offset: 0

Antti Karttunen, Nov 10 2012

nonn

Antti Karttunen, Table of n, a(n) for n = 0..8727

Needed for A218602. Cf. also A218599, A053645, A082853, A002262.

(define (A218601 n) (if (zero? n) n (-1+ (- n (A218600 (-1+ (A213711 n)))))))

a(0)=0, and for n>0, a(n) = (n-A218600(A213711(n)-1))-1.

A082854 Integers 1 to Catalan(n) followed by integers 1 to Catalan(n+1) etc.

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16

Offset: 0

Antti Karttunen, Apr 17 2003

nonn

Cf. A082853, A002260, A000108.

a(n) = A082853(n)+1.

A082327 Permutation of natural numbers induced by the contraction of Catalan bijection signature-permutation A082325.

Original entry on oeis.org

0, 1, 3, 2, 4, 8, 9, 7, 5, 6, 12, 10, 11, 13, 22, 23, 26, 25, 27, 21, 24, 19, 14, 15, 20, 17, 16, 18, 35, 36, 33, 28, 29, 34, 30, 31, 32, 40, 37, 38, 39, 41, 64, 65, 68, 67, 69, 77, 78, 76, 73, 74, 82, 80, 81, 83, 63, 66, 75, 72, 79, 61, 70, 56, 42, 43, 57, 45, 44, 46

Offset: 0

Antti Karttunen, Apr 17 2003

nonn

A. Karttunen, Gatomorphisms (with the complete Scheme source)
Index entries for signature-permutations induced by Catalan automorphisms

Inverse of A082328. a(n) = A072798(A082328(A072798(n))). Cf. also A082329-A082330.

a(n) = A082853(A082325(A081291(n))).

A082328 Permutation of natural numbers induced by the contraction of Catalan bijection signature-permutation A082326.

Original entry on oeis.org

0, 1, 3, 2, 4, 8, 9, 7, 5, 6, 11, 12, 10, 13, 22, 23, 26, 25, 27, 21, 24, 19, 14, 15, 20, 17, 16, 18, 31, 32, 34, 35, 36, 30, 33, 28, 29, 38, 39, 40, 37, 41, 64, 65, 68, 67, 69, 77, 78, 76, 73, 74, 81, 82, 80, 83, 63, 66, 75, 72, 79, 61, 70, 56, 42, 43, 57, 45, 44, 46

Offset: 0

Antti Karttunen, Apr 17 2003

nonn

A. Karttunen, Gatomorphisms (with the complete Scheme source)
Index entries for signature-permutations induced by Catalan automorphisms

Inverse of A082327. a(n) = A072798(A082327(A072798(n))). Cf. also A082329-A082330.

a(n) = A082853(A082326(A081291(n))).

A130918 Simple self-inverse permutation of natural numbers: List each block of A000108(n) numbers from A014137(n-1) to A014138(n-1) in reverse order.

Original entry on oeis.org

0, 1, 3, 2, 8, 7, 6, 5, 4, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 196, 195, 194, 193, 192

Offset: 0

Antti Karttunen, Jun 11 2007

nonn

In principle this involution is the signature permutation of yet another Catalan automorphism. However, the question remains what is the most "natural" way to create such an automorphism acting e.g. on S-expressions (i.e. rooted plane binary trees), which would produce this sequence as its signature permutation.

A. Karttunen, Table of n, a(n) for n = 0..2055
A. Karttunen, Signature permutations of Catalan bijections
Index entries for signature-permutations of Catalan automorphisms

Inverse: A130918. Cf. A054429, A057163. The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A130380 and A036987.

(define (A130918 n) (if (zero? n) n (- (A014138 (- (A072643 n) 1)) (A082853 n))))

a(0)=0, a(n) = A014138(A072643(n)-1) - A082853(n).

cp's OEIS Frontend

A082363 Permutation of natural numbers induced by the contraction of Catalan bijection signature-permutation A082355.

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A082364 Permutation of natural numbers induced by the contraction of Catalan bijection signature-permutation A082356.

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A082361 Permutation of natural numbers induced by the contraction of Catalan bijection signature-permutation A082351.

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A082362 Permutation of natural numbers induced by the contraction of Catalan bijection signature-permutation A082352.

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A218601 After the first zero, integers from 0 to A213709(n)-1 followed by integers from 0 to A213709(n+1)-1, etc.

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A082854 Integers 1 to Catalan(n) followed by integers 1 to Catalan(n+1) etc.

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A082327 Permutation of natural numbers induced by the contraction of Catalan bijection signature-permutation A082325.

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A082328 Permutation of natural numbers induced by the contraction of Catalan bijection signature-permutation A082326.

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A130918 Simple self-inverse permutation of natural numbers: List each block of A000108(n) numbers from A014137(n-1) to A014138(n-1) in reverse order.

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