A152142 a(n) = Product_{k=1..floor((n-1)/2)} (1 + 4*sin(k*Pi/n)^2 + 16*sin(k*Pi/n)^4).

1, 1, 1, 13, 7, 76, 39, 421, 217, 2353, 1216, 13201, 6825, 74101, 38311, 415948, 215047, 2334781, 1207089, 13105441, 6775552, 73562593, 38032081, 412916701, 213479175, 2317756876, 1198287271, 13009880533, 6726147337, 73026206161

Offset

0,4

Links

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (0,7,0,-9,0,7,0,-1).

Formula

G.f.: (x^8 - x^7 - 8*x^6 - 6*x^5 + 9*x^4 + 6*x^3 - 6*x^2 + x + 1) / ((x^4 - x^3 - 3*x^2 - x + 1)*(x^4 + x^3 - 3*x^2 + x + 1)). - Colin Barker, Jan 05 2014

Mathematica

f[n_] = Product[(1 + 4*Sin[k*Pi/n]^2 + 16*Sin[k*Pi/n]^4), {k, 1, Floor[(n - 1)/2]}]; a = Table[f[n], {n, 0, 30}]; Round[a]; FullSimplify[ExpandAll[a]]

Prog

(PARI) Vec((x^8-x^7-8*x^6-6*x^5+9*x^4+6*x^3-6*x^2+x+1)/((x^4-x^3-3*x^2-x+1)*(x^4+x^3-3*x^2+x+1)) + O(x^100)) \\ Colin Barker, Jan 05 2014

Crossrefs

Sequence in context: A345399 A298257 A298928 * A298085 A177427 A110056

Adjacent sequences: A152139 A152140 A152141 * A152143 A152144 A152145

Keyword

nonn,easy

Author

Roger L. Bagula and Gary W. Adamson, Nov 26 2008

Status

approved