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A133558
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a(n)=a(n-1)+9*a(n-2) for n>=2, a(0)=1, a(1)=2 .
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6
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1, 2, 11, 29, 128, 389, 1541, 5042, 18911, 64289, 234488, 813089, 2923481, 10241282, 36552611, 128724149, 457697648, 1616214989, 5735493821, 20281428722, 71900873111, 254433731609, 901541589608, 3191445174089, 11305319480561
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| G.f.: (1+x)/(1-x-9*x^2) .
a(n)=Sum_{k, 0<=k<=n+1}A122950(n+1,k)*8^(n+1-k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 08 2008
a(n)=(1/2)*[(1/2)-(1/2)*sqrt(37)]^n+(1/2)*[(1/2)+(1/2)*sqrt(37)]^n+(3/74)*[(1/2)+(1/2)*sqrt(37)]^n *sqrt(37)-(3/74)*[(1/2)-(1/2)*sqrt(37)]^n*sqrt(37), with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 18 2008]
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MATHEMATICA
| LinearRecurrence[{1, 9}, {1, 2}, 30] (* or *) CoefficientList[Series[ (1+x)/(1-x-9x^2), {x, 0, 30}], x] (* From Harvey P. Dale, Apr 21 2011 *)
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CROSSREFS
| Sequence in context: A092275 A086252 A106926 * A140745 A178629 A062802
Adjacent sequences: A133555 A133556 A133557 * A133559 A133560 A133561
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KEYWORD
| easy,nonn
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 03 2008
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