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A115451
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Expansion of 1/((1+x)*(1-2*x)*(1+x^2)).
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6
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1, 1, 2, 4, 9, 17, 34, 68, 137, 273, 546, 1092, 2185, 4369, 8738, 17476, 34953, 69905, 139810, 279620, 559241, 1118481, 2236962, 4473924, 8947849, 17895697, 35791394, 71582788, 143165577, 286331153, 572662306, 1145324612, 2290649225, 4581298449, 9162596898
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OFFSET
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0,3
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COMMENTS
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Signed version is A077931. Row sums of A115450.
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,1,2).
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FORMULA
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a(n) = a(n-1) + a(n-2) + a(n-3) + 2*a(n-4);
a(n) = Sum_{k=0..n} (2^(n-k+1)-1)(-1)^k} - Sum_{k=0..floor(n/2)} (2^(n-2k)-1)(-1)^k}.
a(n) = A000975(n+1) - A077854(n-1).
a(n) = A112030(n)/10 + (-1)^n/6 +2^(n+3)/15. - R. J. Mathar, Feb 06 2011
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MATHEMATICA
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CoefficientList[Series[1/((1 + x) (1 - 2 x) (1 + x^2)), {x, 0, 50}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 20 2011 *)
LinearRecurrence[{1, 1, 1, 2}, {1, 1, 2, 4}, 50] (* Harvey P. Dale, Oct 22 2011 *)
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PROG
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(PARI) x='x+O('x^50); Vec(1/((1+x)*(1-2*x)*(1+x^2))) \\ G. C. Greubel, Sep 26 2017
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CROSSREFS
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Sequence in context: A088039 A266108 A077931 * A245122 A291728 A268649
Adjacent sequences: A115448 A115449 A115450 * A115452 A115453 A115454
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Jan 22 2006
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STATUS
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approved
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