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Search: id:A099784
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| A099784 |
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Sum C(n-k,2k)2^k*(-2)^(n-3k), k=0..floor(n/3). |
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+0
1
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| 1, -2, 4, -6, 4, 16, -92, 312, -848, 1960, -3824, 5760, -3824, -15392, 88384, -299616, 814144, -1881344, 3669568, -5524608, 3657472, 14807680, -84909824, 287723520, -781639424, 1805843968, -3521371136, 5298829824
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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In general a(n)=sum{k=0..floor(n/3), C(n-k,2k)u^k*v^(n-3k)} has g.f. (1-v*x)/((1-v*x)^2-u*x^2) and satisfies the recurrence a(n)=2uv*a(n-1)-v^2*a(n-2)+u*a(n-3).
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FORMULA
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G.f.: (1+2x)/((1+2x)^2-2x^3); a(n)=sum{k=0..floor(n/3), C(n-k, 2k)2^(n-2k)(-1)^(n-3k); a(n)=-4a(n-1)-4a(n-2)+2a(n-3).
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CROSSREFS
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Sequence in context: A011176 A074320 A014428 this_sequence A082747 A127275 A071288
Adjacent sequences: A099781 A099782 A099783 this_sequence A099785 A099786 A099787
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Oct 26 2004
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