math

Determine the pattern: What comes next?

.1, 1, 2, 4, 7, _

.4, 9, 16, 25,_

Explain. I need help explaining. Thank you.

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  1. First looks like a sort of Fibonacci sequence, where each term is the sum of the three previous terms, making the sequence
    1,1,2,4,7,13,24,44,...

    However, that assumes a leading term of zero.

    The leading .1 throws me off.

    Or, it could be that each term is one less than a Fibonacci number:
    Fib: 1 2 3 5 8 13 21 34 ...
    You: 1 1 2 4 7 12 20 33 ...

    The second one is obviously a sequence of perfect squares. Next is 36.

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