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A099098
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Quadrisection of a Padovan sequence.
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8
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1, 1, 4, 12, 37, 114, 351, 1081, 3329, 10252, 31572, 97229, 299426, 922111, 2839729, 8745217, 26931732, 82938844, 255418101, 786584466, 2422362079, 7459895657, 22973462017, 70748973084, 217878227876, 670976837021, 2066337330754
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OFFSET
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0,3
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COMMENTS
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Quadrisection of sequence with g.f. 1/(1-x^2-x^3), or A000931(n+3).
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LINKS
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FORMULA
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G.f.: (1-x-x^2)/(1-2x-3x^2-x^3);
a(n)=sum{k=0..2n, binomial(k, 4n-2k)};
a(n)=2a(n-1)+3a(n-2)+a(n-3);
a(n) = Sum [k=0..n, C(2n-k, 2k) ].
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EXAMPLE
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1 + x + 4*x^2 + 12*x^3 + 37*x^4 + 114*x^5 + 351*x^6 + ...
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MATHEMATICA
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LinearRecurrence[{2, 3, 1}, {1, 1, 4}, 40] (* Harvey P. Dale, Aug 23 2011 *)
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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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