Number of Straight-Chain Alk*nes of given length A straight-chain alk*ne is defined as a sequence of carbon atoms connected by single (alkane), double (alkene), or triple bonds (alkyne), (implicit hydrogens are used.) Carbon atoms can only form 4 bonds, so no carbon atom may be forced to have more than four bonds. A straight-chain alk*ne can be represented as a list of its carbon-carbon bonds.

These are some examples of valid straight-chain alk*nes:

[]       CH4              Methane
[1]      CH3-CH3          Ethane
[2]      CH2=CH2          Ethene
[3]      CH≡CH            Ethyne
[1,1]    CH3-CH2-CH3      Propane
[1,2]    CH3-CH=CH2       Propene
[1,3]    CH3-C≡CH         Propyne
[2,1]    CH2=CH-CH3       Propene
[2,2]    CH2=C=CH2        Allene (Propadiene)
[3,1]    CH≡C-CH3         Propyne 
[1,1,1]  CH3-CH2-CH2-CH3  Butane
...


While these are not, as at least one carbon atom would have more than 4 bonds:

[2,3]
[3,2]
[3,3]
...


Your task is to create a program/function that, given a positive integer n, outputs/returns the number of valid straight-chain alk*nes of exactly n carbon atoms in length. This is OEIS A077998.

Specifications/Clarifications


You must handle 1 correctly by returning 1.
Alk*nes like [1,2] and [2,1] are considered distinct.
Output is the length of a list of all the possible alk*nes of a given length.
You do not have to handle 0 correctly.


Test Cases:

1 =&gt; 1
2 =&gt; 3
3 =&gt; 6
4 =&gt; 14


This is code golf, so lowest byte count wins!
MATL, 10 bytes
7K5vBiY^1)

Try it online!
Explanation
This uses the characterization found in OEIS

a(n) is the top left entry of the n-th power of the 3 X 3 matrix [1, 1, 1; 1, 0, 0; 1, 0, 1]

7    % Push 7
K    % Push 4
5    % Push 5
v    % Concatenate all numbers into a column vector: [7; 4; 5]
B    % Convert to binary: gives 3×3 matrix [1, 1, 1; 1, 0, 0; 1, 0, 1]
i    % Input n
Y^   % Matrix power
1)   % Take the first element of the resulting matrix, i.e. its upper-left corner.
     % Implicitly display