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A341544
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a(n) = sqrt( Product_{j=1..n} Product_{k=1..4} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/4)^2) ).
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1
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36, 256, 2916, 38416, 527076, 7311616, 101727396, 1416468496, 19727326116, 274760478976, 3826898412516, 53301739046416, 742397156205156, 10340257357947136, 144021201787572516, 2005956552488017936, 27939370476391960356, 389145229905568604416, 5420093847412497929316
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = 19*a(n-1) - 76*a(n-2) + 76*a(n-3) - 19*a(n-4) + a(n-5).
a(n) = 18*a(n-1) - 58*a(n-2) + 18*a(n-3) - a(n-4) + 144.
G.f.: 4*(4 - 67*x + 197*x^2 - 107*x^3 + 9*x^4) / ((1 - x)*(1 - 14*x + x^2)*(1 - 4*x + x^2)).
a(n) = 6 + 4*(2 + sqrt(3))^n + 4*(2 - sqrt(3))^n + (7 + 4*sqrt(3))^n + (7 - 4*sqrt(3))^n. (End)
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MATHEMATICA
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Table[6 + 4 (2 + Sqrt[3])^n + 4 (2 - Sqrt[3])^n + (7 + 4 Sqrt[3])^n + (7 - 4 Sqrt[3])^n, {n, 1, 20}] // FullSimplify (* Vaclav Kotesovec, Feb 14 2021 *)
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PROG
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(PARI) default(realprecision, 120);
a(n) = round(sqrt(prod(j=1, n, prod(k=1, 4, 4*sin((2*j-1)*Pi/(2*n))^2+4*sin((2*k-1)*Pi/4)^2))));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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