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A099156
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2^(n-1)*U(n-1,2).
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3
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0, 1, 8, 60, 448, 3344, 24960, 186304, 1390592, 10379520, 77473792, 578272256, 4316282880, 32217174016, 240472260608, 1794909388800, 13397386067968, 99999450988544, 746406063636480, 5571250705137664, 41584381386555392
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Index entries for sequences related to Chebyshev polynomials.
Index entries for sequences related to linear recurrences with constant coefficients, signature (8,-4).
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FORMULA
| G.f.: x/(1-8x+4x^2); E.g.f.: exp(4x)sinh(2sqrt(3)x)/sqrt(3); a(n)=8a(n-1)-4a(n-2); a(n)=sqrt(3)(1+sqrt(3))^(2n)/12-sqrt(3)(sqrt(3)-1)^(2n)/12; a(n)=sum{k=0..n, binomial(2n, 2k+1)3^k/2}; a(n)=2^(n-1)U(n-1, 4/2) where U is the Chebyshev polynomial of the second kind.
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MATHEMATICA
| Join[{a=0, b=1}, Table[c=8*b-4*a; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 19 2011*)
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PROG
| (Other) sage: [lucas_number1(n, 8, 4) for n in xrange(0, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
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CROSSREFS
| Cf. A090965.
Sequence in context: A094169 A129325 A001267 * A199526 A129331 A005990
Adjacent sequences: A099153 A099154 A099155 * A099157 A099158 A099159
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Oct 01 2004
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