Number of palindrome splits In this task you will take as input a non-negative integer \$n\$, and output the number of pairs of non-negative integers \$a,b\$ such that both are palindromes*, \$a \leq b\$, and \$a+b = n\$.  For example if \$n\$ is \$22\$ then the valid pairs are

\$
\begin{array}{c|c}
a &amp; b  \\
\hline
0 &amp; 22 \\
11 &amp; 11 \\
\end{array}
\$

So the output is \$2\$.

As another example, if \$n\$ is \$145\$  then the valid pairs are

\$
\begin{array}{c|c}
a &amp; b \\
\hline
4 &amp; 141 \\
44 &amp; 101 \\
\end{array}
\$

So the output is 2.

Your submission should be a program or function.  Answers will be scored in bytes with fewer bytes being the goal.

Test Cases

\$
\begin{array}{c|c c|c}
\mathrm{Input} &amp; \mathrm{Output} &amp; \mathrm{Input} &amp; \mathrm{Output} \\
\hline
0 &amp; 1  &amp; 12 &amp; 5\\
1 &amp; 1  &amp; 13 &amp; 4\\
2 &amp; 2  &amp; 14 &amp; 4\\
3 &amp; 2  &amp; 15 &amp; 3\\
4 &amp; 3  &amp; 16 &amp; 3\\
5 &amp; 3  &amp; 17 &amp; 2\\
6 &amp; 4  &amp; 18 &amp; 2\\
7 &amp; 4  &amp; 19 &amp; 1\\
8 &amp; 5  &amp; 20 &amp; 1\\
9 &amp; 5  &amp; 21 &amp; 0\\
10 &amp; 5 &amp; 22 &amp; 2\\
11 &amp; 5 &amp; 23 &amp; 1\\
\end{array}
\$

OEIS A260254



* In base 10
Jelly, 9 bytes

ŻŒḂ€ḋṚ$HĊ


A monadic Link accepting a non-negative integer which yields a non-negative integer.

Try it online!

How?

Counts all pairs without the \$a\leq b\$ restriction, halves and rounds up. Note that the halved count is only a fraction if \$\frac n 2\$ is a palindrome and in such cases we want to count this \$a=b\$ pair.

ŻŒḂ€ḋṚ$HĊ - Link: integer, n    e.g. 22
Ż         - zero-range               [0,1,2,...,9,10,11,12,...,21,22]
   €      - for each:
 ŒḂ       -   is palindrome (digits) [1,1,1,...,1,0,1,0,...0,1]
      $   - last two links as a monad:
     Ṛ    -   reverse                [1,0,...,0,1,0,1,...,1,1,1]
    ḋ     -   dot-product           3  (=1×1+1×0+...+1×0+1×1+0×1+...+0×1+1×1)
       H  - halve                   1.5
        Ċ - ceil                    2