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Search: id:A099625
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| A099625 |
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Sum C(n-k,k+2)2^(n-k-2)(1/2)^k, k=0..floor(n/2). |
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+0
1
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| 0, 0, 1, 6, 25, 88, 281, 842, 2413, 6692, 18101, 48014, 125393, 323376, 825393, 2088850, 5248853, 13110844, 32584653, 80639446, 198844281, 488813768, 1198491913, 2931934938, 7158830781, 17450923092, 42480107365, 103283553054
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OFFSET
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0,4
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COMMENT
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In general a(n)=sum{k=0..floor(n/2), C(n-k,k+2)u^(n-k-2)(v/u)^k has g.f. x^2/((1-u*x)^2(1-u*x-v*x^2)) and satisfies the recurrence a(n)=3u*a(n-1)-(3u^2-v)a(n-2)+(u^3-2uv)a(n-3)+u^2^v*a(n-4).
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FORMULA
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G.f.: x^2/((1-2x)^2(1-2x-x^2)); a(n)=sum{k=0..floor(n/2), C(n-k, k+2)2^(n-2k-2)}; a(n)=6a(n-1)-11a(n-2)+4a(n-3)+4a(n-4).
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CROSSREFS
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Cf. A099623, A099624.
Sequence in context: A133714 A164271 A055585 this_sequence A143628 A056279 A055337
Adjacent sequences: A099622 A099623 A099624 this_sequence A099626 A099627 A099628
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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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