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January 23, 2012–The Wolfram|Alpha Sequence Team 0

What rule gives the integer sequence 3, 10, 17, 18, 7, …? Wolfram|Alpha can easily find that this sequence comes from a simple cubic polynomial, -*x*^{3} + 6*x*^{2} – 4*x* + 2.

A different sequence, 1, 1, 3, 7, 22, 82, 333, 1448, … can be identified as the sequence of the polyhexes. After that, the input sequence of the polyhexes recovers the above sequence.

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