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A056914
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a(n) = Lucas(4*n+1).
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9
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1, 11, 76, 521, 3571, 24476, 167761, 1149851, 7881196, 54018521, 370248451, 2537720636, 17393796001, 119218851371, 817138163596, 5600748293801, 38388099893011, 263115950957276, 1803423556807921, 12360848946698171
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OFFSET
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0,2
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REFERENCES
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V. E. Hoggatt, Jr., Fibonacci and Lucas Numbers, A Publication of the Fibonacci Association, Houghton Mifflin Co., 1969, pp. 27-29.
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LINKS
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FORMULA
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a(n) = 7*a(n-1) - a(n-2), with a(0)=1, a(1)=11.
a(n) = (11*(((7+3*sqrt(5))/2)^n -((7-3*sqrt(5))/2)^n) - (((7+3*sqrt(5))/2)^(n-1) -((7-3*sqrt(5))/2)^(n-1)))/3*sqrt(5).
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MAPLE
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with(combinat); seq(fibonacci(4*n+2)+fibonacci(4*n), n = 0..30); # G. C. Greubel, Jan 16 2020
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MATHEMATICA
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LucasL[4*Range[0, 30]+1] (* or *) LinearRecurrence[{7, -1}, {1, 11}, 30] (* G. C. Greubel, Dec 24 2017 *)
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PROG
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(PARI) my(x='x+O('x^30)); Vec((1+4*x)/(1-7*x+x^2)) \\ G. C. Greubel, Dec 24 2017
(Magma) [Lucas(4*n+1): n in [0..30]]; // G. C. Greubel, Dec 24 2017
(Sage) [lucas_number2(4*n+1, 1, -1) for n in (0..30)] # G. C. Greubel, Jan 16 2020
(GAP) List([0..30], n-> Lucas(1, -1, 4*n+1)[2] ); # G. C. Greubel, Jan 16 2020
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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