PROG
(MAGMAMagma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1+2*(1-x)*x*(1+x)/(1-2*x-8*x^2-2*x^3+x^4) )); // G. C. Greubel, May 15 2019
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Revision History for A152104
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
Quartic product sequence: a(n) = 2^n*Product_{k=1..(n-1)/2} (1 + m*cos(k*Pi/n)^2 + q*cos(k*Pi/n)^4), with m=6, q=4.
(history; published version)
(history; published version)
STATUS
reviewed
approved
STATUS
proposed
reviewed
STATUS
editing
proposed
NAME
Quartic product sequence: a(n) = 2^n*productProduct_{k=1..(n-1)/2} (1 + m*cos(k*Pi/n)^2 + lq*cos(k*Pi/n)^4, k=1..(n-1)/2), with m=6, lq=4.
COMMENTS
a(n+1)/a(n) tends to 1/2*(1 + sqrt(11) + sqrt(2*(4+sqrt(11)))) /2 = 4.070983928708143809... - Vaclav Kotesovec, Nov 30 2012
FORMULA
G.f.: 1 + 2*(1-x)*x*(1+x)/(1-2*x-8*x^2-2*x^3+x^4). - Vaclav Kotesovec, Nov 30 2012
MATHEMATICA
With[{m = 6; l , q = 4; b = }, Table[2^n*Round[Product[1 + m*Cos[k*Pi/n]^2 + lq*Cos[k*Pi/n]^4, {k, 1, (n - 1)/2}], ], {n, 0, 30}]; FullSimplify[ExpandAll[%]] Round[b] (* modified by _G. C. Greubel_, May 15 2019 *)
PROG
(PARI) my(x='x+O('x^30)); Vec(1+2*(1-x)*x*(1+x)/(1-2*x-8*x^2-2*x^3+x^4)) \\ G. C. Greubel, May 15 2019
(MAGMA) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1+2*(1-x)*x*(1+x)/(1-2*x-8*x^2-2*x^3+x^4) )); // G. C. Greubel, May 15 2019
(Sage) (1+2*(1-x)*x*(1+x)/(1-2*x-8*x^2-2*x^3+x^4)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 15 2019
STATUS
approved
editing
STATUS
editing
approved
NAME
Quartic product sequence: m = 6; l = 4; a(n) = 2^n*Product[product(1 + m*Cos[cos(k*Pi/n])^2 + l*Cos[cos(k*Pi/n])^4, {k, =1, ..(n - 1)/2}]), with m=6, l=4.
FORMULA
m = 6; l = 4; a(n)=2^n*Product[1 + m*Cos[k*Pi/n]^2 + l*Cos[k*Pi/n]^4, {k, 1, (n - 1)/2}].
KEYWORD
nonn,easy,changed
STATUS
approved
editing
STATUS
reviewed
approved
STATUS
proposed
reviewed
STATUS
editing
proposed