Wythoff's Losing Pairs up to Fifty
In Wythoff's game two piles are given. A move removes any positive number of counters from one pile, or the same positive number from both. The player who takes the last counter wins. Count the unordered pairs {a, b} with 1 ≤ a ≤ b ≤ 50 such that the player to move loses with optimal play from piles (a, b). Answer with an integer.
Related problems
Source: Wythoff's game (1907); the Beatty-sequence structure is classical. Statement written for AxiomIQ.