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Search: id:A081571
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| A081571 |
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Sixth binomial transform of F(n+1). |
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+0
2
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| 1, 7, 50, 363, 2669, 19814, 148153, 1113615, 8402722, 63577171, 481991621, 3659227062, 27808295345, 211479529943, 1609093780114, 12247558413819, 93245414394973, 710040492168070, 5407464407991017, 41185377124992351
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OFFSET
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0,2
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COMMENT
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Binomial transform of A081570. Case k=6 of family of recurrences a(n)=(2k+1)a(n-1)-A028387(k-1)a(n-2),a(0)=1,a(1)=k+1.
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FORMULA
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a(n)=13a(n-1)-41a(n-2), a(0)=1, a(1)=7. a(n)=(1/2 - sqrt(5)/10)(13/2 - sqrt(5)/2)^n + (sqrt(5)/10 + 1/2)*(sqrt(5)/2 + 13/2)^n. G.f.: (1-6x)/(1-13x+41x^2).
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CROSSREFS
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Cf. A000045.
Adjacent sequences: A081568 A081569 A081570 this_sequence A081572 A081573 A081574
Sequence in context: A033125 A022037 A054413 this_sequence A081189 A108869 A065429
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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), Mar 22 2003
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