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Search: id:A099782
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| A099782 |
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Sum C(n-k,2k)2^k*4^(n-3k), k=0..floor(n/3). |
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+0
1
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| 1, 4, 16, 66, 280, 1216, 5380, 24144, 109504, 500488, 2300128, 10612224, 49096720, 227578432, 1056304384, 4907373600, 22813275520, 106100835328, 493609021504, 2296885357824, 10689540189184, 49753373831296, 231588118339072
(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.: (1-4x)/((1-4x)^2-2x^3); a(n)=8a(n-1)-16a(n-2)+2a(n-3).
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CROSSREFS
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Sequence in context: A081915 A026762 A082307 this_sequence A109034 A110276 A026883
Adjacent sequences: A099779 A099780 A099781 this_sequence A099783 A099784 A099785
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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 26 2004
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