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A122910
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Expansion of (1-2x-3x^2)/((1-2x)(1+4x)(1-8x)).
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1
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1, 4, 45, 302, 2636, 20184, 165040, 1305952, 10504896, 83809664, 671394560, 5367485952, 42954566656, 343577810944, 2748857364480, 21989919383552, 175923113148416, 1407369872769024, 11259019111628800, 90071912374730752
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OFFSET
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0,2
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COMMENTS
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Let M be the matrix M(n,k)=J(k+1)*sum{j=0..n, (-1)^(n-j)C(n,j)C(j+1,k+1)}. a(n) gives the row sums of M^3.
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LINKS
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Table of n, a(n) for n=0..19.
Index to sequences with linear recurrences with constant coefficients, signature (6,24,-64).
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FORMULA
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G.f.: (1-2x-3x^2)/(1-6x-24x^2+64x^3); a(n)=5*8^n/8+7*(-4)^n/24+2^n/12; a(n)=J(n)*A083424(n-1)+J(n+1)*A083424(n) where J(n) are the Jacobsthal numbers A001045(n).
a(0)=1, a(1)=4, a(2)=45, a(n)=6*a(n-1)+24*a(n-2)-64*a(n-3) [From Harvey P. Dale, June 21 2011]
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MATHEMATICA
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CoefficientList[Series[(1-2x-3x^2)/((1-2x)(1+4x)(1-8x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{6, 24, -64}, {1, 4, 45}, 30] (* From Harvey P. Dale, June 21 2011 *)
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CROSSREFS
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Sequence in context: A132998 A120075 A123650 * A117644 A055602 A073565
Adjacent sequences: A122907 A122908 A122909 * A122911 A122912 A122913
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Sep 18 2006
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STATUS
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approved
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