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Search: id:A099621
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| A099621 |
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Sum C(n-k,k+1)3^(n-k-1)(4/3)^k, k=0..floor(n/2). |
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+0
2
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| 0, 1, 6, 31, 144, 637, 2730, 11467, 47508, 194953, 794574, 3222583, 13023192, 52491349, 211161138, 848231779, 3403688796, 13647040225, 54685016022, 219030629455, 876994213920, 3510591943981, 14050213040826, 56224387958011
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OFFSET
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0,3
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COMMENT
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In general a(n)=sum{k=0..floor(n/2),C(n-k,k+1)u^(n-k-1)(v/u)^(k-1)} has g.f. x^2/((1-u*x)(1-u*x-v*x^2)) and satisfies the recurrence a(n)=2u*a(n-1)-(u^2-v)a(n-2)-u*v*a(n-3).
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FORMULA
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G.f.: x^2/((1-3x)(1-3x-4x^2)); a(n)=6a(n-1)-5a(n-2)-12a(n-3).
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CROSSREFS
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Cf. A094705, A099622.
Sequence in context: A009076 A012714 A094951 this_sequence A056015 A128740 A026705
Adjacent sequences: A099618 A099619 A099620 this_sequence A099622 A099623 A099624
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Oct 25 2004
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