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A165310
a(0)=1, a(1)=3, a(n) = 7*a(n-1) - 9*a(n-2) for n > 1.
4
1, 3, 12, 57, 291, 1524, 8049, 42627, 225948, 1197993, 6352419, 33684996, 178623201, 947197443, 5022773292, 26634636057, 141237492771, 748950724884, 3971517639249, 21060066950787, 111676809902268, 592197066758793
OFFSET
0,2
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. - John M. Campbell, Jul 08 2011
FORMULA
G.f.: (1-4x)/(1-7x+9x^2).
a(n) = Sum_{k=0..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). - Klaus Brockhaus, Sep 26 2009
MATHEMATICA
LinearRecurrence[{7, -9}, {1, 3}, 30] (* Harvey P. Dale, Sep 23 2011 *)
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
CROSSREFS
Sequence in context: A110309 A263667 A101106 * A133158 A328295 A194089
KEYWORD
nonn
AUTHOR
Philippe Deléham, Sep 14 2009
STATUS
approved