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A306472
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a(n) = 37*27^n.
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1
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37, 999, 26973, 728271, 19663317, 530909559, 14334558093, 387033068511, 10449892849797, 282147106944519, 7617971887502013, 205685240962554351, 5553501505988967477, 149944540661702121879, 4048502597865957290733, 109309570142380846849791, 2951358393844282864944357
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OFFSET
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0,1
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COMMENTS
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x = a(n) and y = A002042(n) satisfy the Lebesgue-Ramanujan-Nagell equation x^2 + 3^(6*n+1) = 4*y^3 (see Theorem 2.1 in Chakraborty, Hoque and Sharma).
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LINKS
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FORMULA
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O.g.f.: 37/(1 - 27*x).
E.g.f.: 37*exp(27*x).
a(n) = 27*a(n-1) for n > 0.
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EXAMPLE
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For a(0) = 37 and A002042(0) = 7, 37^2 + 3 = 1372 = 4*7^3.
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MAPLE
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a:=n->37*27^n: seq(a(n), n=0..20);
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MATHEMATICA
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37*27^Range[0, 20]
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PROG
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(GAP) List([0..20], n->37*27^n);
(Magma) [37*27^n: n in [0..20]];
(PARI) a(n) = 37*27^n;
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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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