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A015533
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a(n) = 4*a(n-1) + 9*a(n-2).
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11
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0, 1, 4, 25, 136, 769, 4300, 24121, 135184, 757825, 4247956, 23812249, 133480600, 748232641, 4194255964, 23511117625, 131792774176, 738771155329, 4141219588900, 23213818753561, 130126251314344, 729429374039425
(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 4'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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FORMULA
| O.g.f.: x/(1-4*x-9*x^2). a(n)=-9^n*(A^n-B^n)/(2*sqrt(13)) where A=-1/(2+sqrt(13)) and B=1/(sqrt(13)-2) . - R. J. Mathar, Apr 29 2008
a(n)=Sum_{k, 0<=k<=n}A155161(n,k)*3^(n-k), n>=1 . [From Philippe DELEHAM, Jan 27 2009]
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MATHEMATICA
| a[n_]:=(MatrixPower[{{1, 4}, {1, -5}}, n].{{1}, {1}})[[2, 1]]; Table[Abs[a[n]], {n, -1, 40}] [From Vladimir Orlovsky, Feb 19 2010]
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PROG
| (Sage) [lucas_number1(n, 4, -9) for n in xrange(0, 22)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
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CROSSREFS
| Sequence in context: A013582 A123660 A156701 * A079291 A173612 A072221
Adjacent sequences: A015530 A015531 A015532 * A015534 A015535 A015536
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KEYWORD
| nonn,easy
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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