A079221 -id:A079221 - cp's OEIS frontend

A079217 Triangle T(n,d) (listed row-wise: T(1,1)=1, T(2,1)=1, T(2,2)=1, T(3,1)=2, T(3,2)=0, T(3,3)=1, ...) giving the number of n-edge general plane trees with root degree d that are fixed by Catalan Automorphisms A057511/A057512 (Deep rotation of general parenthesizations/plane trees).

1, 1, 1, 2, 0, 1, 3, 1, 0, 1, 5, 0, 0, 0, 1, 6, 2, 1, 0, 0, 1, 10, 0, 0, 0, 0, 0, 1, 11, 5, 0, 1, 0, 0, 0, 1, 18, 0, 2, 0, 0, 0, 0, 0, 1, 21, 11, 0, 0, 1, 0, 0, 0, 0, 1, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 35, 26, 3, 2, 0, 1, 0, 0, 0, 0, 0, 1, 68, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 69, 66, 0, 0, 0, 0, 1, 0, 0

Offset: 0

Antti Karttunen Jan 03 2002

Index entries for sequences related to parenthesizing

The row sums equal to the left edge shifted left once = A057546 = first row of A079216 (the latter gives the Maple procedure PFixedByA057511).

Cf. A079218, A079219, A079220, A079221, A079222 and A003056 and A002262.

[seq(A079217(n),n=0..119)]; A079217 := n -> PFixedByA057511(A003056(n)+1,1, A002262(n)+1);

A079222 Triangle T(n,d) (listed row-wise: T(1,1)=1, T(2,1)=1, T(2,2)=1, T(3,1)=2, T(3,2)=2, T(3,3)=1, ...) giving the number of n-edge general plane trees with root degree d that are fixed by the six-fold application of Catalan Automorphisms A057511/A057512 (Deep rotation of general parenthesizations/plane trees).

Original entry on oeis.org

1, 1, 1, 2, 2, 1, 5, 5, 3, 1, 14, 14, 9, 0, 1, 38, 42, 28, 2, 0, 1, 111, 124, 90, 0, 0, 6, 1, 332, 379, 285, 5, 0, 27, 0, 1, 1029, 1178, 914, 0, 0, 110, 0, 0, 1, 3232, 3742, 2955, 14, 1, 429, 0, 0, 0, 1, 10374, 12024, 9666, 0, 0, 1614, 0, 0, 0, 0, 1, 33679, 39200, 31853, 42, 0

Offset: 0

Antti Karttunen Jan 03 2002

Note: the counts given here are inclusive, i.e. T(n,d) includes also the counts A079218(n,d) and A079219(n,d).

The row sums equal to the left edge shifted left once = A079227 = sixth row of A079216 (the latter gives the Maple procedure PFixedByA057511). Cf. also A079217-A079221 and A003056 & A002262.

[seq(A079222(n),n=0..119)]; A079222 := n -> PFixedByA057511(A003056(n)+1,6, A002262(n)+1);

A079226 Number of Catalan objects fixed by five-fold application of the Catalan bijections A057511/A057512 (deep rotation of general parenthesizations/plane trees).

Original entry on oeis.org

1, 1, 2, 3, 5, 6, 15, 36, 108, 301, 814, 2080, 5223, 12919, 32557, 83943, 222591, 600252, 1632814, 4440240, 12043224, 32572225, 88081208, 238722759, 649725756, 1776546687, 4877740703, 13432630929, 37063472432, 102389547753

Offset: 0

Antti Karttunen Jan 03 2002

nonn

The fifth row of A079216. The leftmost edge of the triangle A079221 and also its row sums shifted by one. Occurs in A073202 as row 9259542121261050623. Cf. A057546, A079223-A079227.

Maple
```
A079226 := n -> A079216bi(n,5);
```

a(n) = A079216(n, 5)

cp's OEIS Frontend

A079217 Triangle T(n,d) (listed row-wise: T(1,1)=1, T(2,1)=1, T(2,2)=1, T(3,1)=2, T(3,2)=0, T(3,3)=1, ...) giving the number of n-edge general plane trees with root degree d that are fixed by Catalan Automorphisms A057511/A057512 (Deep rotation of general parenthesizations/plane trees).

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A079226 Number of Catalan objects fixed by five-fold application of the Catalan bijections A057511/A057512 (deep rotation of general parenthesizations/plane trees).

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