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A248924
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Sequence derived from arithmetic relations between powers of phi (A001622): a(n) = phi^n - (-1)^n * (n - phi^-n).
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0
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2, 2, 1, 7, 3, 16, 12, 36, 39, 85, 113, 210, 310, 534, 829, 1379, 2191, 3588, 5760, 9368, 15107, 24497, 39581, 64102, 103658, 167786, 271417, 439231, 710619, 1149880, 1860468, 3010380, 4870815, 7881229, 12752009, 20633274, 33385246, 54018558, 87403765
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OFFSET
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0,1
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LINKS
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FORMULA
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a(n) = phi^n - (-1)^n * (n - phi^-n), phi = (1 + sqrt(5))/2 = A001622.
G.f.: (2*x+1)*(x^2-2)/((x^2+x-1)*(x+1)^2). - Alois P. Heinz, Oct 17 2014
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EXAMPLE
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a(7) = phi^7 + (n - phi^-7) = 36; a(10) = phi^10 - (n - phi^-10) = 113.
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MATHEMATICA
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LinearRecurrence[{-1, 2, 3, 1}, {2, 2, 1, 7}, 40] (* Harvey P. Dale, Sep 21 2023 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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