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A341545 a(n) = sqrt( Product_{j=1..n} Product_{k=1..6} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/6)^2) ). 1
200, 2916, 80000, 2775556, 105125000, 4115479104, 163146144200, 6498349262596, 259309319120000, 10354620147583716, 413585320648104200, 16521137110112348224, 659981119616472888200, 26365103950427540487396, 1053246219256801250000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..15.

Index entries for linear recurrences with constant coefficients, signature (77, -2002, 24596, -165165, 653835, -1598883, 2483481, -2483481, 1598883, -653835, 165165, -24596, 2002, -77, 1)

FORMULA

a(n) = 77*a(n-1) - 2002*a(n-2) + 24596*a(n-3) - 165165*a(n-4) + 653835*a(n-5) - 1598883*a(n-6) + 2483481*a(n-7) - 2483481*a(n-8) + 1598883*a(n-9) - 653835*a(n-10) + 165165*a(n-11) - 24596*a(n-12) + 2002*a(n-13) - 77*a(n-14) + a(n-15).

a(n) = 76*a(n-1) - 1926*a(n-2) + 22670*a(n-3) - 142495*a(n-4) + 511340*a(n-5) - 1087543*a(n-6) + 1395938*a(n-7) - 1087543*a(n-8) + 511340*a(n-9) - 142495*a(n-10) + 22670*a(n-11) - 1926*a(n-12) + 76*a(n-13) - a(n-14) - 2160.

G.f.: 4*(50*x - 3121*x^2 + 63967*x^3 - 616453*x^4 + 3219563*x^5 - 9827161*x^6 + 18330389*x^7 - 21405307*x^8 + 15754967*x^9 - 7241797*x^10 + 2026187*x^11 - 329569*x^12 + 28911*x^13 - 1182*x^14 + 16*x^15) / ((1 - x)*(1 - 7*x + x^2)*(1 - 6*x + x^2)*(1 - 3*x + x^2)* (1 - 42*x + 83*x^2 - 42*x^3 + x^4)*(1 - 18*x + 43*x^2 - 18*x^3 + x^4)). - Vaclav Kotesovec, Feb 14 2021

PROG

(PARI) default(realprecision, 120);

a(n) = round(sqrt(prod(j=1, n, prod(k=1, 6, 4*sin((2*j-1)*Pi/(2*n))^2+4*sin((2*k-1)*Pi/6)^2))));

CROSSREFS

Column k=6 of A341533.

Sequence in context: A202966 A218846 A219425 * A297318 A200892 A220390

Adjacent sequences:  A341542 A341543 A341544 * A341546 A341547 A341548

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Feb 14 2021

STATUS

approved

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Last modified December 1 08:44 EST 2021. Contains 349426 sequences. (Running on oeis4.)