A082854 -id:A082854 - cp's OEIS frontend

A082853 Integers 0 to Catalan(n)-1 followed by integers 0 to Catalan(n+1)-1 etc.

0, 0, 0, 1, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

Offset: 0

Antti Karttunen, Apr 17 2003

nonn

Harvey P. Dale, Table of n, a(n) for n = 0..1000

a(n) = A082854(n)-1. Cf. A002262, A000108.

Table[Range[0,CatalanNumber[n]-1],{n,0,6}]//Flatten (* Harvey P. Dale, Jul 24 2021 *)

a(n) = n - A082852(n)

A085197 Positions of ones in A007001. Repeating part in each sub-permutation A082315[A014137(n-1)..A014138(n-1)] normalized to begin from 1.

Original entry on oeis.org

1, 3, 6, 8, 11, 15, 17, 20, 22, 25, 29, 31, 34, 38, 43, 45, 48, 50, 53, 57, 59, 62, 64, 67, 71, 73, 76, 80, 85, 87, 90, 92, 95, 99, 101, 104, 108, 113, 115, 118, 122, 127, 133, 135, 138, 140, 143, 147, 149, 152, 154, 157, 161, 163, 166, 170, 175, 177, 180, 182, 185, 189

Offset: 1

Antti Karttunen, Jun 14 2003. Proposed by Wouter Meeussen Mar 15 2003

nonn

From the second term 3 onward also one more than the partial sums of A076050.

Paolo Xausa, Table of n, a(n) for n = 1..16796
Antti Karttunen, Notes concerning A080237-tree and related sequences.

Cf. A085196. First column of A085180.

PositionIndex[Nest[Flatten[Map[Range[#+1] &, #]] &, {1}, 6]][[1]] (* Paolo Xausa, Mar 04 2024 *)

a(n) = A080336(n-1) + n = A082854(A082315(A072795(A081291(n-1)))).

a(n) = n if n < 2, otherwise a(n-1)+A076050(n-1).

A082329 Permutation of positive natural numbers: a(n) = A082327(n-1)+1.

Original entry on oeis.org

1, 2, 4, 3, 5, 9, 10, 8, 6, 7, 13, 11, 12, 14, 23, 24, 27, 26, 28, 22, 25, 20, 15, 16, 21, 18, 17, 19, 36, 37, 34, 29, 30, 35, 31, 32, 33, 41, 38, 39, 40, 42, 65, 66, 69, 68, 70, 78, 79, 77, 74, 75, 83, 81, 82, 84, 64, 67, 76, 73, 80, 62, 71, 57, 43, 44, 58, 46, 45, 47

Offset: 1

Antti Karttunen, Apr 17 2003

nonn

Index entries for sequences that are permutations of the natural numbers

Inverse of A082330. a(n) = A082854(A082325(A081291(n-1))).

A082330 Permutation of positive natural numbers: a(n) = A082328(n-1)+1.

Original entry on oeis.org

1, 2, 4, 3, 5, 9, 10, 8, 6, 7, 12, 13, 11, 14, 23, 24, 27, 26, 28, 22, 25, 20, 15, 16, 21, 18, 17, 19, 32, 33, 35, 36, 37, 31, 34, 29, 30, 39, 40, 41, 38, 42, 65, 66, 69, 68, 70, 78, 79, 77, 74, 75, 82, 83, 81, 84, 64, 67, 76, 73, 80, 62, 71, 57, 43, 44, 58, 46, 45, 47

Offset: 1

Antti Karttunen, Apr 17 2003

nonn

Index entries for sequences that are permutations of the natural numbers

Inverse of A082329. a(n) = A082854(A082326(A081291(n-1))).

cp's OEIS Frontend

A082853 Integers 0 to Catalan(n)-1 followed by integers 0 to Catalan(n+1)-1 etc.

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A085197 Positions of ones in A007001. Repeating part in each sub-permutation A082315[A014137(n-1)..A014138(n-1)] normalized to begin from 1.

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A082329 Permutation of positive natural numbers: a(n) = A082327(n-1)+1.

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A082330 Permutation of positive natural numbers: a(n) = A082328(n-1)+1.

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