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A099234
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A trisection of 1/(1-x-x^4).
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3
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1, 1, 4, 10, 26, 69, 181, 476, 1252, 3292, 8657, 22765, 59864, 157422, 413966, 1088589, 2862617, 7527704, 19795288, 52054840, 136886433, 359964521, 946583628, 2489191330, 6545722210, 17213011605, 45264335853, 119029728628
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| A row of A099233.
Row sums of number triangle A116089. - Paul Barry (pbarry(AT)wit.ie), Feb 04 2006
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FORMULA
| G.f.: 1/(1-x(1+x)^3); a(n)=sum{k=0..n, binomial(3(n-k), k)}; a(n)=a(n-1)+3a(n-2)+3a(n-3)+a(n-4); a(n)=A003269(3n).
a(n)=sum{k=0..n, C(3k,n-k)}=sum{k=0..n, C(n,k)C(4k,n)/C(4k,k)}. - Paul Barry (pbarry(AT)wit.ie), Feb 04 2006
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MATHEMATICA
| CoefficientList[Series[1/(1-x (1+x)^3), {x, 0, 30}], x] (* or *) LinearRecurrence[{1, 3, 3, 1}, {1, 1, 4, 10}, 30] (* From Harvey P. Dale, June 05 2011 *)
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CROSSREFS
| Sequence in context: A200051 A200663 A200464 * A087222 A130583 A105999
Adjacent sequences: A099231 A099232 A099233 * A099235 A099236 A099237
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Oct 08 2004
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