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A097041
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Expansion of (1+x)/(1-x^2-9*x^3).
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2
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1, 1, 1, 10, 10, 19, 100, 109, 271, 1009, 1252, 3448, 10333, 14716, 41365, 107713, 173809, 479998, 1143226, 2044279, 5463208, 12333313, 23861719, 61502185, 134861536, 276257656, 688381201, 1490011480, 3174700105, 7685442289
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = a(n-2) + 9*a(n-3).
a(n) = Sum_{k=0..floor(n/2)} binomial(floor((n-k)/2), k)*9^k.
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MATHEMATICA
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CoefficientList[Series[(1+x)/(1-x^2-9x^3), {x, 0, 30}], x] (* or *) LinearRecurrence[{0, 1, 9}, {1, 1, 1}, 30] (* Harvey P. Dale, Mar 12 2015 *)
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PROG
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(PARI) x='x+O('x^50); Vec((1+x)/(1-x^2-9*x^3)) \\ G. C. Greubel, Apr 30 2017
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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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