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A077411
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Combined Diophantine Chebyshev sequences A077409 and A077250.
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2
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7, 11, 59, 103, 583, 1019, 5771, 10087, 57127, 99851, 565499, 988423, 5597863, 9784379, 55413131, 96855367, 548533447, 958769291, 5429921339, 9490837543, 53750679943, 93949606139, 532076878091, 930005223847, 5267018100967
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OFFSET
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0,1
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COMMENTS
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a(n)^2 - 24*b(n)^2 = 25, with the companion sequence b(n)= A077410(n).
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LINKS
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FORMULA
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G.f.: (1-x)*(7+18*x+7*x^2)/(1-10*x^2+x^4).
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EXAMPLE
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59 = a(2) = sqrt(24*A077410(2)^2 + 25) = sqrt(24*12^2 + 25)= sqrt(3481) = 59.
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MATHEMATICA
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CoefficientList[Series[(1-x)*(7+18*x+7*x^2)/(1-10*x^2+x^4), {x, 0, 50}], x] (* or *) LinearRecurrence[{0, 10, 0, -1}, {7, 11, 59, 103}, 30] (* G. C. Greubel, Jan 18 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec((1-x)*(7+18*x+7*x^2)/(1-10*x^2+x^4)) \\ G. C. Greubel, Jan 18 2018
(Magma) I:=[7, 11, 59, 103]; [n le 4 select I[n] else 10*Self(n-2) - Self(n-4): n in [1..30]]; // G. C. Greubel, Jan 18 2018
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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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