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Search: id:A127840
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| A127840 |
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a(1)=1,a(2)=...=a(6)=0,a(n)=a(n-6)+a(n-5) for n>6. |
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+0
1
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| 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 1, 0, 0, 1, 3, 3, 1, 0, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 2, 6, 15, 20, 15, 7, 8, 21, 35, 35, 22, 15, 29, 56, 70, 57, 37, 44, 85, 126, 127, 94, 81, 129, 211, 253, 221, 175, 210, 340, 464, 474
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OFFSET
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1,18
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COMMENT
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Part of the phi_k family of sequences defined by a(1)=1,a(2)=...=a(k)=0, a(n)=a(n-k)+a(n-k+1) for n>k. phi_2 is a shift of the Fibonacci sequence and phi_3 is a shift of the Padovan sequence.
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REFERENCES
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S. Suter, Binet-like formulas for recurrent sequences with characteristic equation x^k=x+1, preprint, 2007
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FORMULA
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Binet-like formula: a(n)=sum_{i=1...6} (r_i^n)/(5(r_i)^2+6(r_i)) where r_i is a root of x^6=x+1
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CROSSREFS
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Sequence in context: A159854 A144225 A017837 this_sequence A145153 A076837 A055363
Adjacent sequences: A127837 A127838 A127839 this_sequence A127841 A127842 A127843
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KEYWORD
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nonn
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AUTHOR
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Stephen Suter (sms5064(AT)psu.edu), Apr 02 2007
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