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A075269
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Product of Lucas numbers and inverted Lucas numbers: a(n)=A000032(n)*A075193(n).
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2
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2, -3, 12, -28, 77, -198, 522, -1363, 3572, -9348, 24477, -64078, 167762, -439203, 1149852, -3010348, 7881197, -20633238, 54018522, -141422323, 370248452, -969323028, 2537720637, -6643838878, 17393796002, -45537549123, 119218851372, -312119004988, 817138163597
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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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G.f.: (2+x+2x^2)/((1+3x+x^2)(1-x)).
a(n) = -3a(n-1) - a(n-2)+5 = -2a(n-1) + 2a(n-2) + a(n-3) = a(-1-n). (End)
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MATHEMATICA
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CoefficientList[Series[(2 + x + 2x^2)/(1 + 2x - 2x^2 - x^3), {x, 0, 30}], x]
LinearRecurrence[{-2, 2, 1}, {2, -3, 12}, 30] (* Harvey P. Dale, Jun 30 2022 *)
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PROG
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(PARI) a(n)=1+(-1)^n*(fibonacci(2*n)+fibonacci(2*n+2))
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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Mario Catalani (mario.catalani(AT)unito.it), Sep 11 2002
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STATUS
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approved
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