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A002534
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a(n) = 2*a(n-1) + 9*a(n-2).
(Formerly M2058 N0814)
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13
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0, 1, 2, 13, 44, 205, 806, 3457, 14168, 59449, 246410, 1027861, 4273412, 17797573, 74055854, 308289865, 1283082416, 5340773617, 22229288978, 92525540509, 385114681820, 1602959228221, 6671950592822, 27770534239633, 115588623814664
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| For n>=2, a(n) equals the permanent of the (n-1)X(n-1) tridiagonal matrix with 2's along the main diagonal, and 3's along the superdiagonal and the subdiagonal. [From John M. Campbell, Jul 19 2011]
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REFERENCES
| N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A. Tarn, Approximations to certain square roots and the series of numbers connected therewith, Mathematical Questions and Solutions from the Educational Times, 1 (1916), 8-12.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
| E.g.f.: exp(x)*sinh(sqrt(10)*x)/sqrt(10); a(n)=sum{k=0..n, binomial(n, 2*k+1)*10^k}. - Paul Barry, Sep 29 2004
a(n)=((1+sqrt(10))^n-(1-sqrt(10))^n)/(2*sqrt(10)) - Artur Jasinski, Dec 10 2006
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MAPLE
| A002534:=-z/(-1+2*z+9*z**2); [S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Table[((1 + Sqrt[10])^n - (1 - Sqrt[10])^n)/(2 Sqrt[10]), {n, 0, 30}]] (* Artur Jasinski, Dec 10 2006 *)
LinearRecurrence[{2, 9}, {0, 1}, 30] (* T. D. Noe, Aug 18 2011 *)
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PROG
| (Sage) [lucas_number1(n, 2, -9) for n in xrange(0, 20)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
(MAGMA) [Ceiling(((1+Sqrt(10))^n-(1-Sqrt(10))^n)/(2*Sqrt(10))): n in [0..30]]; // Vincenzo Librandi, Aug 15 2011
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CROSSREFS
| Sequence in context: A102296 A025194 A084156 * A117717 A176060 A168172
Adjacent sequences: A002531 A002532 A002533 * A002535 A002536 A002537
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Johannes W. Meijer, Aug 18 2011
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