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A105745
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For n>2, a(n) > 0 is such that a(n-1)^2+4*a(n-2)*a(n) is a minimal square, a(1)=1, a(2)=12.
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1
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1, 12, 13, 4, 9, 9, 4, 5, 6, 8, 8, 6, 2, 4, 6, 4, 2, 2, 4, 6, 4, 2, 2, 4, 6, 4, 2, 2, 4, 6, 4, 2, 2, 4, 6, 4, 2, 2, 4, 6, 4, 2, 2, 4, 6, 4, 2, 2, 4, 6, 4, 2, 2, 4, 6, 4, 2, 2, 4, 6, 4, 2, 2, 4, 6, 4, 2, 2, 4, 6, 4, 2, 2, 4, 6, 4, 2, 2, 4, 6, 4, 2, 2, 4, 6, 4, 2, 2, 4, 6, 4, 2, 2, 4, 6, 4, 2, 2, 4
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: x*(4*x^16 + 4*x^15 + 2*x^14 + 2*x^13 + 3*x^12 - 2*x^11 + x^10 + x^9 - 2*x^8 + 8*x^7 + 8*x^6 - 8*x^5 - 9*x^4 - 4*x^3 - 13*x^2 - 12*x - 1)/(x^5 - 1). - Chai Wah Wu, May 07 2024
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MAPLE
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A[1]:= 1: A[2]:= 12:
for n from 3 to 100 do
R:= map(rhs@op, [msolve(y^2=A[n-1]^2, 4*A[n-2])]);
ys:= map(t -> (floor((A[n-1]-t)/(4*A[n-2]))+1)*4*A[n-2]+t, R);
A[n]:= (min(ys)^2-A[n-1]^2)/(4*A[n-2]);
od:
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CROSSREFS
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KEYWORD
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nonn,easy,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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