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A165310
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a(0)=1, a(1)=3, a(n)=7*a(n-1)-9*a(n-2) for n>1 .
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3
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1, 3, 12, 57, 291, 1524, 8049, 42627, 225948, 1197993, 6352419, 33684996, 178623201, 947197443, 5022773292, 26634636057, 141237492771, 748950724884, 3971517639249, 21060066950787, 111676809902268, 592197066758793
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n)/a(n-1) tends to (7+sqrt(13))/2 = 5.30277563...= 2+A098316.
For n>=2, a(n) equals 3^n times the permanent of the (2n-2)X(2n-2) matrix with 1/sqrt(3)'s along the main diagonal, and 1's along the superdiagonal and the subdiagonal. [From John M. Campbell, Jul 08 2011]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..100
Index to sequences with linear recurrences with constant coefficients, signature (7,-9).
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FORMULA
| G.f.: (1-4x)/(1-7x+9x^2). a(n)=Sum_{k, 0<=k<=n}A165253(n,k)*3^(n-k).
a(n) = ((13-sqrt(13))*(7+sqrt(13))^n+(13+sqrt(13))*(7-sqrt(13))^n )/(26*2^n). [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 26 2009]
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MATHEMATICA
| LinearRecurrence[{7, -9}, {1, 3}, 30] (* From Harvey P. Dale, Sep 23 2011 *)
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PROG
| (MAGMA) I:=[1, 3]; [n le 2 select I[n] else 7*Self(n-1)-9*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Sep 24 2011
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CROSSREFS
| Sequence in context: A027140 A110309 A101106 * A133158 A194089 A178807
Adjacent sequences: A165307 A165308 A165309 * A165311 A165312 A165313
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KEYWORD
| nonn
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 14 2009
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