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#23 by Joerg Arndt at Sat Aug 28 04:47:34 EDT 2021
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#22 by Hugo Pfoertner at Sat Aug 28 04:10:56 EDT 2021
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#21 by Michel Marcus at Sat Aug 28 03:24:20 EDT 2021
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#20 by Michel Marcus at Sat Aug 28 03:24:15 EDT 2021
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| COMMENTS
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a(n) = F(n)*P(n) + F(n+1)*P(n+1) for F(n) = A000045(n) the Fibonacci numbers and P(n) = A000129(n) the Pell numbers.
a(n) = ) is the numerator of the continued fraction [1,...,1,2,...,2] with n 1's followed by n 2's.
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| FORMULA
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a(n) = F(n)*P(n) + F(n+1)*P(n+1) for F(n) = A000045(n) the Fibonacci numbers and P(n) = A000129(n) the Pell numbers.
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| STATUS
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approved
editing
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#19 by Michel Marcus at Sat Aug 28 03:23:47 EDT 2021
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#18 by Joerg Arndt at Sat Aug 28 03:07:22 EDT 2021
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#17 by Michel Marcus at Wed Aug 18 04:59:37 EDT 2021
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#16 by Michel Marcus at Wed Aug 18 04:59:34 EDT 2021
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| PROG
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(PARI) P(n) = ([2, 1; 1, 0]^n)[2, 1]; \\ A000129
a(n) = fibonacci(n)*P(n)+ fibonacci(n+1)*P(n+1); \\ Michel Marcus, Aug 18 2021
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| STATUS
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proposed
editing
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#15 by Kevin Ryde at Tue Aug 17 19:44:40 EDT 2021
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#14 by Kevin Ryde at Tue Aug 17 19:44:30 EDT 2021
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| LINKS
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<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,7,2,-1).
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| STATUS
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proposed
editing
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