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A051958
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a(n) = 2 a(n-1) + 24 a(n-2), a(0)=0, a(1)=1.
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9
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0, 1, 2, 28, 104, 880, 4256, 29632, 161408, 1033984, 5941760, 36699136, 216000512, 1312780288, 7809572864, 47125872640, 281681494016, 1694383931392, 10149123719168, 60963461791744, 365505892843520, 2194134868688896
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OFFSET
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0,3
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COMMENTS
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The ratio a(n+1)/a(n) converges to 6 as n approaches infinity. - Felix P. Muga II, Mar 10 2014
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REFERENCES
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F. P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, March 2014; Preprint on ResearchGate.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (2,24).
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FORMULA
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G.f.: x/((1+4*x)*(1-6*x)).
a(n) = (6^n - (-4)^n)/10.
a(n) = 2^(n-1)*A015441(n).
a(n+1) = Sum_{k = 0..n} A238801(n,k)*5^k. - Philippe Deléham, Mar 07 2014
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MATHEMATICA
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Join[{a=0, b=1}, Table[c=2*b+24*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
CoefficientList[Series[x / ((1 + 4 x) (1 - 6 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Mar 08 2014 *)
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PROG
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(PARI) a(n)=(6^n-(-4)^n)/10
(MAGMA) [(6^n-(-4)^n)/10: n in [0..25]]; // Vincenzo Librandi, Mar 08 2014
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CROSSREFS
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Cf. A015441.
Sequence in context: A200040 A334696 A281201 * A123807 A213829 A164834
Adjacent sequences: A051955 A051956 A051957 * A051959 A051960 A051961
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KEYWORD
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easy,nonn
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AUTHOR
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Barry E. Williams, Jan 04 2000
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STATUS
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approved
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