Narayana-Zidek-Capell numbers Generate the nth Narayana-Zidek-Capell number given an input n. Fewest bytes win.

f(1)=1, f(n) is the sum of the previous floor(n/2) Narayana-Zidek-Capell terms.

Test Cases:

f(1)=1

f(9)=42

f(14)=1308

f(15)=2605

f(23)=664299
Ruby, 34 32 bytes

This uses a formula from the OEIS page for the Narayana-Zidek-Cappell numbers.

Edit: Got rid of parentheses using operator precedence with thanks to feersum and Neil.

f=-&gt;x{x&lt;4?1:2*f[x-1]-x%2*f[x/2]}