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A099232
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a(n)=2a(n-1)+2a(n-2)-3a(n-3).
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0
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0, 1, 2, 6, 13, 32, 72, 169, 386, 894, 2053, 4736, 10896, 25105, 57794, 133110, 306493, 705824, 1625304, 3742777, 8618690, 19847022, 45703093, 105244160, 242353440, 558085921, 1285146242, 2959404006, 6814842733, 15693054752, 36137582952
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Partial sums of A006130 (with leading zero).
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FORMULA
| G.f.: x/((1-x)(1-x-3x^2)); a(n)=sum{k=0..floor(n/2), binomial(n-k, k+1)3^k}; a(n)=(1/2+sqrt(13)/2)^n(1/6+7sqrt(13)/78)+(1/6-7sqrt(13)/78)(1/2-sqrt(13)/2)^n-1/3.
a(n+1)=sum{k=0..n, C(k+1,n-k+1)3^(n-k)}; - Paul Barry (pbarry(AT)wit.ie), May 21 2006
a(n) = a(n-1) + 3*a(n-2) + 1, n>1 [From Gary Detlefs (gdetlefs(AT)aol.com), Jun 21 2010]
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CROSSREFS
| Sequence in context: A094687 A018013 A062424 * A053562 A003039 A109385
Adjacent sequences: A099229 A099230 A099231 * A099233 A099234 A099235
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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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