<a href= "/index/Rec#order_03" >Indextosequenceswithentriesforlinear recurrences with constant coefficients</a>, signature (21,-84,64).

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(PARI) a(n) = polchebyshev(4, 2, 2^n) \\Michel Marcus,May 03 2015

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5, 209, 3905, 64769, 1045505, 16764929, 268386305, 4294770689, 68718690305, 1099508482049, 17592173461505, 281474926379009, 4503599426043905, 72057593232621569, 1152921501385621505,18446744060824649729,295147905127813218305,4722366482663486783489

Colin Barker, <a href= "/A020541/b020541.txt ">Table of n, a(n) for n = 0..829</a>

<a href= "/index/Rec#order_03" >Index to sequences with linear recurrences with constant coefficients</a>, signature (21,-84,64).

a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-3) for n>2. -Colin Barker,May 03 2015

G.f.: (64*x^2-104*x-5) / ((x-1)*(4*x-1)*(16*x-1)). -Colin Barker,May 03 2015

(PARI) Vec((64*x^2-104*x-5)/((x-1)*(4*x-1)*(16*x-1)) + O(x^100)) \\Colin Barker,May 03 2015

nonn,easy

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a(n)=4th Chebyshev polynomial (second kind) evaluated atpowersof2^n.

a(n)=16^(n+1) - 3*4^(n+1) + 1.

Table[ChebyshevU[4, 2^n], {n, 1, 40}][From_(*_Vladimir Joseph Stephan Orlovsky_, Nov 03 2009]*)

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