模式

序列

OEIS序列

说明

$S_n\left(\text{<munder accentunder="true"> 3 <mo> \_ </mo> </munder> <munder accentunder="true"> 2 <mo> \_ </mo> </munder> <munder accentunder="true"> 1 <mo> \_ </mo> </munder>},\text{<munder accentunder="true"> 3 <mo> \_ </mo> </munder> <munder accentunder="true"> 1 <mo> \_ </mo> </munder> 2}\right)$

$1,2,4,9,21,51,\cdots$

A001006

Motzkin数

$S_n^1\left(\text{<munder accentunder="true"> 3 <mo> \_ </mo> </munder> <munder accentunder="true"> 2 <mo> \_ </mo> </munder> <munder accentunder="true"> 1 <mo> \_ </mo> </munder>},\text{<munder accentunder="true"> 3 <mo> \_ </mo> </munder> <munder accentunder="true"> 1 <mo> \_ </mo> </munder> 2}\right)$

$0,\text{1},\text{1},\text{3},\text{6},\text{15},\text{36,}\cdots$

A005043

Riordan数

$S_n\left(\text{<munder accentunder="true"> 1 <mo> \_ </mo> </munder> <munder accentunder="true"> 2 <mo> \_ </mo> </munder> 3},\text{<munder accentunder="true"> 3 <mo> \_ </mo> </munder> <munder accentunder="true"> 1 <mo> \_ </mo> </munder> 2}\right)$

$\text{1},\text{2},\text{4},\text{7},\text{11},\text{16},\text{22,}\cdots$

A152947

$a_n=1+\frac{n\left(n-1\right)}{2}$

$S_n^1\left(\text{<munder accentunder="true"> 1 <mo> \_ </mo> </munder> <munder accentunder="true"> 2 <mo> \_ </mo> </munder> 3},\text{<munder accentunder="true"> 3 <mo> \_ </mo> </munder> <munder accentunder="true"> 1 <mo> \_ </mo> </munder> 2}\right)$

$\text{1},\text{2},\text{4},\text{7},\text{11},\text{16},\text{22,}\cdots$

A152947

$a_n=n-1\left(n\ge 1\right)$

$S_n^1\left(\text{<munder accentunder="true"> 1 <mo> \_ </mo> </munder> <munder accentunder="true"> 2 <mo> \_ </mo> </munder> 3},\text{3 <munder accentunder="true"> 1 <mo> \_ </mo> </munder> <munder accentunder="true"> 2 <mo> \_ </mo> </munder>}\right)$

$\text{1},\text{2},\text{3},\text{4},\text{5},\cdots$

A000027

$a_n=n-1\left(n\ge 2\right)$

$S_n\left(\text{<munder accentunder="true"> 1 <mo> \_ </mo> </munder> <munder accentunder="true"> 2 <mo> \_ </mo> </munder> 3},\text{3 <munder accentunder="true"> 1 <mo> \_ </mo> </munder> <munder accentunder="true"> 2 <mo> \_ </mo> </munder>}\right)$

$\text{1},\text{2},\text{4},\text{8},\text{16},\text{32},\text{64,}\cdots$

A011782

$a_n=2^n{}^{-1}$

$S_n\left(\text{<munder accentunder="true"> 2 <mo> \_ </mo> </munder> <munder accentunder="true"> 1 <mo> \_ </mo> </munder> 3},\text{<munder accentunder="true"> 3 <mo> \_ </mo> </munder> <munder accentunder="true"> 1 <mo> \_ </mo> </munder> 2}\right)$

$\text{1},\text{2},\text{4},\text{8},\text{16},\text{32},\text{64,}\cdots$

A011782

$a_n=2^n{}^{-1}$

$S_n^1\left(\text{<munder accentunder="true"> 2 <mo> \_ </mo> </munder> <munder accentunder="true"> 1 <mo> \_ </mo> </munder> 3},\text{<munder accentunder="true"> 3 <mo> \_ </mo> </munder> <munder accentunder="true"> 1 <mo> \_ </mo> </munder> 2}\right)$

$\text{1},\text{3},\text{7},\text{15},\text{31},\cdots$

A153010

$a_n=2^n{}^{-1}-1\left(n\ge 2\right)$