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A090139
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a(n) = 10*a(n-1) - 20*a(n-2), a(0)=1,a(1)=5.
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8
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1, 5, 30, 200, 1400, 10000, 72000, 520000, 3760000, 27200000, 196800000, 1424000000, 10304000000, 74560000000, 539520000000, 3904000000000, 28249600000000, 204416000000000, 1479168000000000, 10703360000000000
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OFFSET
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0,2
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COMMENTS
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Fifth binomial transform of (1, 0, 5, 0, 25, 0, ...).
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LINKS
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FORMULA
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a(n) = ((5-sqrt(5))^n + (5+sqrt(5))^n)/2.
a(n) = Sum_{k=0..floor(n/2)} C(n, 2k) * 5^(n-k).
a(n) = Sum_{k=0..n} C(n, k) * 5^(n-k/2) * (1+(-1)^k)/2.
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MATHEMATICA
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LinearRecurrence[{10, -20}, {1, 5}, 30] (* G. C. Greubel, Aug 02 2019 *)
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PROG
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(PARI) my(x='x+O('x^30)); Vec((1-5*x)/(1-10*x+20*x^2)) \\ G. C. Greubel, Aug 02 2019
(Magma) I:=[1, 5]; [n le 2 select I[n] else 10*Self(n-1) -20*Self(n-2): n in [1..30]]; // G. C. Greubel, Aug 02 2019
(Sage) ((1-5*x)/(1-10*x+20*x^2)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Aug 02 2019
(GAP) a:=[1, 5];; for n in [3..30] do a[n]:=10*a[n-1]-20*a[n-2]; od; a; # G. C. Greubel, Aug 02 2019
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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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