A082856 -id:A082856 - cp's OEIS frontend

A082857 Inverse function of N -> N injection A082856.

0, 1, 0, 2, 0, 3, 0, 6, 0, 0, 0, 4, 0, 0, 0, 14, 0, 0, 0, 0, 0, 7, 0, 16, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, 5, 0, 0, 0, 15, 0, 0, 0, 11, 0, 0, 0, 39, 0, 0, 0, 0, 0, 0, 0, 43, 0, 0, 0, 0, 0, 0, 0, 123, 0, 0, 0, 0, 0, 8, 0, 19, 0, 0, 0, 0, 0, 0, 0, 51, 0, 0, 0, 0, 0, 20, 0, 53, 0, 0, 0, 0, 0, 0, 0, 154, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, 151, 0, 0, 0, 0, 0, 0, 0, 155

Offset: 0

Antti Karttunen, May 06 2003

nonn

a(n) = 0 for those n which do not occur as the values of A082856. All positive natural numbers occur here once.

Antti Karttunen, Alternative Catalan Orderings (with the complete Scheme source)

Cf. A082856, A072634-A072637, A075173-A075174.

a(A082856(n)) = n for all n.

A082858 Array A(x,y): the greatest common subtree (intersect) of the binary trees x and y, (x,y) running as (0,0),(1,0),(0,1),(2,0),(1,1),(0,2) and each index referring to a binary tree encoded by A014486(j).

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 2, 3, 2, 1, 0, 0, 1, 2, 1, 1, 2, 1, 0, 0, 1, 2, 1, 4, 1, 2, 1, 0, 0, 1, 1, 3, 2, 2, 3, 1, 1, 0, 0, 1, 1, 3, 2, 5, 2, 3, 1, 1, 0, 0, 1, 2, 3, 1, 2, 2, 1, 3, 2, 1, 0, 0, 1, 2, 1, 1, 1, 6, 1, 1, 1, 2, 1, 0, 0, 1, 2, 1, 4, 1, 3, 3, 1, 4, 1, 2, 1, 0, 0, 1, 2, 1, 4, 2, 3, 7, 3, 2, 4, 1, 2, 1, 0

Offset: 0

Antti Karttunen, May 06 2003

Note that together with A082860 this forms a distributive lattice, thus it is possible to compute this function also with the binary AND-operation (A004198) with the help of appropriate mapping functions. I.e. we have A(x,y) = A082857(A004198(A082856(x), A082856(y))).

Antti Karttunen, Alternative Catalan Orderings (with the complete Scheme source)
Index entries for sequences related to lattices

Cf. A072764. The lower/upper triangular region: A082859. Cf. A080300, A025581, A002262.

A082860 Array A(x,y): the least common supertree (union) of the binary trees x and y, (x,y) running as (0,0),(1,0),(0,1),(2,0),(1,1),(0,2) and each index referring to a binary tree encoded by A014486(j).

Original entry on oeis.org

0, 1, 1, 2, 1, 2, 3, 2, 2, 3, 4, 3, 2, 3, 4, 5, 4, 6, 6, 4, 5, 6, 5, 4, 3, 4, 5, 6, 7, 6, 5, 14, 14, 5, 6, 7, 8, 7, 6, 15, 4, 15, 6, 7, 8, 9, 8, 16, 6, 11, 11, 6, 16, 8, 9, 10, 9, 19, 7, 14, 5, 14, 7, 19, 9, 10, 11, 10, 9, 8, 42, 15, 15, 42, 8, 9, 10, 11, 12, 11, 10, 37, 51, 43, 6, 43, 51, 37, 10, 11, 12, 13, 12, 11, 38, 9, 52, 16, 16, 52, 9, 38, 11, 12, 13, 14, 13, 12

Offset: 0

Antti Karttunen, May 06 2003

Note that together with A082858 this forms a distributive lattice, thus it is possible to compute this function also with the binary OR-operation (A003986) with the help of appropriate mapping functions. I.e. we have A(x,y) = A082857(A003986(A082856(x), A082856(y))).

Antti Karttunen, Alternative Catalan Orderings (with the complete Scheme source)
Index entries for sequences related to lattices

The lower/upper triangular region: A082861. Cf. A072764, A080300, A025581, A002262.

cp's OEIS Frontend

A082857 Inverse function of N -> N injection A082856.

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A082858 Array A(x,y): the greatest common subtree (intersect) of the binary trees x and y, (x,y) running as (0,0),(1,0),(0,1),(2,0),(1,1),(0,2) and each index referring to a binary tree encoded by A014486(j).

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A082860 Array A(x,y): the least common supertree (union) of the binary trees x and y, (x,y) running as (0,0),(1,0),(0,1),(2,0),(1,1),(0,2) and each index referring to a binary tree encoded by A014486(j).

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