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A114203
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Row sums of a Pascal-Jacobsthal triangle.
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2
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1, 2, 4, 8, 18, 44, 110, 272, 662, 1596, 3838, 9240, 22286, 53812, 129974, 313888, 757878, 1829644, 4416910, 10662952, 25742302, 62147556, 150038438, 362226480, 874493446, 2111213372, 5096916094, 12305037368, 29706982638, 71719002644
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OFFSET
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0,2
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COMMENTS
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Binomial transform of double Jacobsthal sequence 1,1,1,1,3,3,5,5,11,11,... Row sums of A114202.
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LINKS
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FORMULA
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G.f.: (1-x)^2/(1 - 4x + 5x^2 - 2x^3 - 2x^4);
a(n) = 4a(n-1) - 5a(n-2) + 2a(n-3) + 2a(n-4);
a(n) = Sum_{k=0..n} Sum_{i=0..n-k} C(n-k, i)*C(k, i)*J(i);
a(n) = Sum_{k=0..n} C(n, k)*J(floor((k+2)/2)), J(n)=A001045(n).
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MATHEMATICA
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LinearRecurrence[{4, -5, 2, 2}, {1, 2, 4, 8}, 40] (* Harvey P. Dale, Jun 05 2012 *)
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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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