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Search: id:A073313
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| A073313 |
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Binomial transform of generalized Lucas numbers S(n)=S(n-1)+S(n-2)+S(n-3), S(0)=3,S(1)=1,S(2)=3. |
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+0
2
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| 3, 4, 8, 22, 64, 184, 524, 1488, 4224, 11992, 34048, 96672, 274480, 779328, 2212736, 6282592, 17838080, 50647424, 143802560, 408296704, 1159271424, 3291504000, 9345523712, 26534621696, 75339399936, 213910160384, 607352285184
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Limit as n-> infinity of a(n)/a(n-1) is 1+c, where c=1.83928675...
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REFERENCES
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H. Prodinger, "Some information about the Binomial transform", The Fibonacci Quarterly, 32, 1994, 412-415.
N. J. A. Sloane and S. Plouffe, The Encyclopedia of Integer Sequences, Academic Press, San Diego, 1995.
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LINKS
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M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210.
H. Prodinger, Some information about the binomial transform., The Fibonacci Quarterly, 32, 1994, 412-415.
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FORMULA
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a(n) is the trace of the n-th power of 3*3 matrix: first row (2, 1, 0), second row (1, 1, 1), third row (1, 0, 1). It satisfies recurrence a(n)=4*a(n-1)-4*a(n-2)+ 2*a(n-3), a(0)=3, a(1)=4, a(2)=8. Generating function: (3-8x+4x^2)/(1-4x+4x^2-2x^3).
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MATHEMATICA
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f[x_] := f[x]=4*f[x-1]-4*f[x-2]+2*f[x-3]; f[0]=3; f[1]=4; f[2]=8
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CROSSREFS
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Cf. A001644.
Sequence in context: A129285 A051440 A101932 this_sequence A155701 A119529 A096847
Adjacent sequences: A073310 A073311 A073312 this_sequence A073314 A073315 A073316
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KEYWORD
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easy,nonn
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AUTHOR
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Mario Catalani (mario.catalani(AT)unito.it), Jul 26 2002
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 30 2002
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