JEE Delight | B Stat/ B Math | ISI | UGB 2023 | Q5 | P&C | Arrangement of tiles in a row

JEE Delight | B Stat/ B Math | ISI | UGB 2023 | Q5 | P&C | Arrangement of tiles in a row

There is a rectangular plot of size 1 × n. This has to be covered by three
types of tiles - red, blue and black. The red tiles are of size 1 × 1, the blue
tiles are of size 1 × 1 and the black tiles are of size 1 × 2. Let tn denote
the number of ways this can be done. For example, clearly t1 = 2 because
we can have either a red or a blue tile. Also, t2 = 5 since we could have
tiled the plot as: two red tiles, two blue tiles, a red tile on the left and a
blue tile on the right, a blue tile on the left and a red tile on the right, or
a single black tile.
(a) Prove that t2n+1 = tn(tn−1 + tn+1) for all

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[adarsh_pandey]

Sir how I can complete it's theory part ??