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A105063
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a(1)=0, a(2)=0, a(3)=8, a(4)=24, a(n) = 32 + 66*a(n-2) - a(n-4) for n > 4.
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3
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0, 0, 8, 24, 560, 1616, 36984, 106664, 2440416, 7038240, 161030504, 464417208, 10625572880, 30644497520, 701126779608, 2022072419144, 46263741881280, 133426135166016, 3052705837384904, 8804102848537944, 201432321525522416
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OFFSET
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1,3
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COMMENTS
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This sequence has the property 17*a(n)*(a(n) + 1) + 1 is a square.
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LINKS
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FORMULA
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a(n) = a(n-1) +66*a(n-2) -66*a(n-3) -a(n-4) +a(n-5).
G.f.: 8*x^3*(1+x)^2/((1-x)*(1+8*x-x^2)*(1-8*x-x^2)). (End)
a(n) = (1/4)*(-32*[n=0] - 2 + i^n*((23 + 11*(-1)^n)*ChebyshevU(n, 4*I) - i*(187 + 89*(-1)^n)*ChebyshevU(n-1, 4*I))). - G. C. Greubel, Mar 13 2023
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MATHEMATICA
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LinearRecurrence[{1, 66, -66, -1, 1}, {0, 0, 8, 24, 560}, 40] (* G. C. Greubel, Mar 13 2023 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Integers(), 40); [0, 0] cat Coefficients(R!( 8*x^3*(1+x)^2/((1-x)*(1-66*x^2+x^4)) )); // G. C. Greubel, Mar 13 2023
(SageMath)
@CachedFunction
def a(n):
if (n<6): return (0, 0, 0, 8, 24, 560)[n]
else: return a(n-1) +66*a(n-2) -66*a(n-3) -a(n-4) +a(n-5)
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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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