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A098601
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Expansion of (1+2x)/((1+x)(1-x^2-x^3)).
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2
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1, 1, 0, 3, 0, 4, 2, 5, 5, 8, 9, 14, 16, 24, 29, 41, 52, 71, 92, 124, 162, 217, 285, 380, 501, 666, 880, 1168, 1545, 2049, 2712, 3595, 4760, 6308, 8354, 11069, 14661, 19424, 25729, 34086, 45152, 59816, 79237, 104969, 139052, 184207, 244020, 323260
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Diagonal sums of A098599.
The signed sequence 1,-1,0,-3,0,-4,... gives the diagonal sums of A100218. - Paul Barry (pbarry(AT)wit.ie), Nov 09 2004
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (-1,1,2,1).
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FORMULA
| G.f.: x/((1+x)(1-x^2-x^3))+1/(1-x^2-x^3); a(n)=sum{k=0..floor(n/2), binomial(k, n-2k)+binomial(k-1, n-2k-1)}.
a(n)=-a(n-1)+a(n-2)+2a(n-3)+a(n-4).
Inverse binomial transform of A135364. - Paul Curtz (bpcrtz(AT)free.fr), Apr 25 2008
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MATHEMATICA
| CoefficientList[Series[(1+2x)/((1+x)(1-x^2-x^3)), {x, 0, 50}], x] (* or *) LinearRecurrence[{-1, 1, 2, 1}, {1, 1, 0, 3}, 50] (* From Harvey P. Dale, Dec 14 2011 *)
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CROSSREFS
| Cf. A000931, A077883.
Sequence in context: A077150 A065453 A152770 * A113486 A108572 A104686
Adjacent sequences: A098598 A098599 A098600 * A098602 A098603 A098604
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 17 2004
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