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A115451
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Expansion of 1/((1+x)(1-2x)(1+x^2)).
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4
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Signed version is A077931. Row sums of A115450.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,1,1,2).
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FORMULA
| a(n)=a(n)=a(n-1)+a(n-2)+a(n-3)+2a(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
| CoefficientList[Series[1/((1 + x) (1 - 2 x) (1 + x^2)), {x, 0, 50}], x] (* From Vladimir Joseph Stephan Orlovsky, Jun 20 2011 *)
LinearRecurrence[{1, 1, 1, 2}, {1, 1, 2, 4}, 50] (* From Harvey P. Dale, Oct 22 2011 *)
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CROSSREFS
| Sequence in context: A007502 A088039 A077931 * A136326 A059973 A030035
Adjacent sequences: A115448 A115449 A115450 * A115452 A115453 A115454
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jan 22 2006
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