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A182754
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a(1) = 1, a(2) = 21, a(n) = 77*a(n-2) for n>=3.
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7
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1, 21, 77, 1617, 5929, 124509, 456533, 9587193, 35153041, 738213861, 2706784157, 56842467297, 208422380089, 4376869981869, 16048523266853, 337018988603913, 1235736291547681, 25950462122501301, 95151694449171437, 1998185583432600177, 7326680472586200649
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OFFSET
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1,2
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COMMENTS
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For n >= 3, a(n) = the smallest number h > a(n-1) such that [[a(n-2) + a(n-1)] * [a(n-2) + a(n)] * [a(n-1) + a(n)]] / [a(n-2) * a(n-1) * a(n)] is integer (= 104).
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LINKS
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FORMULA
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a(2*n) = 21*a(2*n-1), a(2*n+1) = (11/3)*a(2*n).
G.f.: x*(1+21*x) / ( 1 - 77*x^2 ).
a(n) = 3*7^(n/2)*11^(n/2-1) for n even.
a(n) = 77^((n-1)/2) for n odd.
(End)
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EXAMPLE
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For n = 4; a(2) = 21, a(3) = 77, a(4) = 1617 before [(21+77)*(21+1617)*(77+1617)] / (21*77*1617) = 104.
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MATHEMATICA
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LinearRecurrence[{0, 77}, {1, 21}, 30] (* Harvey P. Dale, Sep 05 2013 *)
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PROG
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(PARI) A182754(n)=if(n%2, 77^(n\2), 77^(n\2-1)*21)
(Magma) I:=[1, 21]; [n le 2 select I[n] else 77*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 11 2018
(PARI) Vec(x*(1 + 21*x) / (1 - 77*x^2) + O(x^40)) \\ Colin Barker, Jan 11 2018
(Python)
def aupton(nn):
dmo = [1, 21, 77]
for n in range(3, nn+1): dmo.append(77*dmo[-2])
return dmo[:nn]
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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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EXTENSIONS
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STATUS
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approved
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