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 ).

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.

Links

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (1,7,6,-8,-6,7,-1,-1).

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

Adjacent sequences: A152113 A152114 A152115 * A152117 A152118 A152119

Keyword

nonn,easy

Author

Roger L. Bagula and Gary W. Adamson, Nov 24 2008

Status

approved