One of the polynomials obtained by taking powers of the Brahmagupta matrix. They satisfy the recurrence relation
(1)
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(2)
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A list of many others is given by Suryanarayan (1996). Explicitly,
(3)
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(4)
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The Brahmagupta polynomials satisfy
(5)
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(6)
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The first few polynomials are
(7)
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(8)
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(9)
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(10)
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(11)
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and
(12)
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(13)
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(14)
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(15)
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(16)
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Taking and gives equal to the Pell numbers and equal to half the Pell-Lucas numbers. The Brahmagupta polynomials are related to the Morgan-Voyce polynomials, but the relationship given by Suryanarayan (1996) is incorrect.