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A077245
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Bisection (even part) of Chebyshev sequence with Diophantine property.
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4
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1, 10, 79, 622, 4897, 38554, 303535, 2389726, 18814273, 148124458, 1166181391, 9181326670, 72284431969, 569094129082, 4480468600687, 35274654676414, 277716768810625, 2186459495808586, 17213959197658063
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OFFSET
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0,2
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COMMENTS
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3*b(n)^2 - 5*a(n)^2 = 7, with the companion sequence b(n)= A077246(n).
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LINKS
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FORMULA
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a(n)= 8*a(n-1) - a(n-2), a(-1) := -2, a(0)=1.
a(n)= S(n, 8)+2*S(n-1, 8), with S(n, x) := U(n, x/2), Chebyshev's polynomials of the 2nd kind, A049310. S(-1, x) := 0 and S(n, 8)= A001090(n+1).
G.f.: (1+2*x)/(1-8*x+x^2).
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EXAMPLE
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5*a(1)^2 + 7 = 5*10^2 + 7 = 507 = 3*13^2 = 3*A077246(1)^2.
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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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