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A099167
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G.f.: (1+x^2)/((1-3x)(1-x-x^2)).
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1
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1, 4, 15, 49, 154, 473, 1437, 4340, 13067, 39277, 117954, 354061, 1062505, 3188036, 9564951, 28696217, 86090858, 258276145, 774834213, 2324511988, 6973551091, 20920677749, 62762072850, 188286282629, 564858951569, 1694577022468
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OFFSET
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0,2
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COMMENTS
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A Lucas convolution.
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LINKS
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FORMULA
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a(n)=4a(n-1)-2a(n-2)-3a(n-3); a(n)=2*3^n-Fib(n+2); a(n)=sum{k=0..n, (L(k)-0^k)3^(n-k)}.
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MATHEMATICA
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CoefficientList[Series[(1+x^2)/((1-3x)(1-x-x^2)), {x, 0, 40}], x] (* or *) LinearRecurrence[ {4, -2, -3}, {1, 4, 15}, 40] (* Harvey P. Dale, Mar 10 2023 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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