Solution
$$1+2^2=5 x^2 + (x-1)$$
$$2+3^2=11=x^2 + (x-1)$$
$$3+4^2=19=x^2 + (x-1)$$
$$4+5^2=29=x^2 + (x-1)$$
$$5+6^2=41=x^2 + (x-1)$$
$$6+7^2=55=x^2 + (x-1)$$
from this we concluded that
$$x^2 + x - 1$$
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