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Search: id:A099579
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| A099579 |
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Sum C(n-k,k-1)3^(k-1), k=0..floor(n/2). |
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+0
2
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| 0, 0, 1, 1, 7, 10, 40, 70, 217, 427, 1159, 2440, 6160, 13480, 32689, 73129, 173383, 392770, 919480, 2097790, 4875913, 11169283, 25856071, 59363920, 137109280, 315201040, 727060321, 1672663441, 3855438727, 8873429050, 20444528200
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OFFSET
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0,5
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COMMENT
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In general a(n)=sum{k=0..floor(n/2), C(n-k,k-1)r^(k-1)} has g.f. x^2/((1-r*x^2)(1-x-r*x^2)), and satisfies the recurrence a(n)=a(n-1)+2r*a(n-2)-r*a(n-3)-r^2*a(n-4).
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FORMULA
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G.f.: x^2/((1-3x^2)(1-x-3x^2)); a(n)=a(n-1)+6a(n-2)-3a(n-3)-9a(n-4).
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CROSSREFS
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Cf. A097038, A099580.
Sequence in context: A119169 A095756 A126076 this_sequence A056521 A056510 A013398
Adjacent sequences: A099576 A099577 A099578 this_sequence A099580 A099581 A099582
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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 23 2004
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