A152103 a(n) = 2^n*Product_{k=1..floor((n-1)/2)} (1 + 2*cos(k*Pi/n)^2 + 4*cos(k*Pi/n)^4).

1, 2, 4, 14, 48, 158, 532, 1778, 5952, 19922, 66676, 223166, 746928, 2499950, 8367268, 28005026, 93732096, 313718882, 1050008932, 3514352558, 11762446512, 39368602238, 131765686708, 441016322834, 1476070150464, 4940368363442

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (2,4,2,-1).

Formula

From Colin Barker, Jan 05 2014: (Start)

a(n) = 2*a(n-1) + 4*a(n-2) + 2*a(n-3) - a(n-4) for n > 5.

G.f.: (x^4-4*x^3-4*x^2+1) / (x^4-2*x^3-4*x^2-2*x+1). (End)

Mathematica

m = 2; l = 4; b = Table[2^n*Product[1 + m*Cos[k*Pi/n]^2 + l*Cos[k*Pi/n]^4, {k, 1, (n - 1)/2}], {n, 0, 30}]; FullSimplify[ExpandAll[%]] Round[b]

Prog

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

Crossrefs

Sequence in context: A062868 A054936 A006443 * A102879 A032312 A032222

Adjacent sequences: A152100 A152101 A152102 * A152104 A152105 A152106

Keyword

nonn,easy

Author

Roger L. Bagula, Nov 24 2008

Status

approved