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A152116
Sixth degree product sequence: a(n) = product( 1 +4*cos(k*Pi/n)^2 +16*cos(k*Pi/n)^4 +64*cos(k*Pi/n)^6, k=1..(n-1)/2 ).
0
1, 1, 1, 4, 15, 45, 160, 533, 1785, 6052, 20295, 68441, 230400, 775657, 2612233, 8794980, 29614935, 99718277, 335764960, 1130580029, 3806834625, 12818225732, 43161016271, 145329992177, 489349324800, 1647717131025, 5548126370513
OFFSET
0,4
COMMENTS
Limiting ration at n=30: 3.367159464464469.
FORMULA
G.f.: (x^4 -2*x^3 +x^2 +2*x +1) * (x^4 +2*x^3 -4*x^2 -2*x +1) / (x^8 +x^7 -7*x^6 +6*x^5 +8*x^4 -6*x^3 -7*x^2 -x +1). - Colin Barker, Oct 23 2013
MATHEMATICA
a = Table[Product[1 + 4*Cos[k*Pi/n]^2 + 16*Cos[k*Pi/n]^4 + 64*Cos[k*Pi/n]^6, {k, 1, (n - 1)/2}], {n, 0, 30}]; Round[%] FullSimplify[ExpandAll[a]]
PROG
(PARI) a(n) = round(prod(k=1, (n-1)/2, 1+4*cos(k*Pi/n)^2+16*cos(k*Pi/n)^4+64*cos(k*Pi/n)^6)) \\ Colin Barker, Oct 23 2013
CROSSREFS
Sequence in context: A062827 A074448 A297088 * A195688 A111038 A188716
KEYWORD
nonn,easy
AUTHOR
STATUS
approved