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Search: id:A127841
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| A127841 |
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a(1)=1, a(2)=...=a(7)=0, a(n)=a(n-7)+a(n-6) for n>7. |
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+0
1
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| 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 3, 3, 1, 0, 0, 1, 4, 6, 4, 1, 0, 1, 5, 10, 10, 5, 1, 1, 6, 15, 20, 15, 6, 2, 7, 21, 35, 35, 21, 8, 9, 28, 56, 70, 56, 29, 17, 37, 84, 126, 126, 85, 46, 54, 121, 210, 252, 211
(list; graph; listen)
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OFFSET
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1,21
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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...7} (r_i^n)/(6(r_i)^2+7(r_i)) where r_i is a root of x^7=x+1
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MAPLE
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P:=proc(n) local a, a0, a1, a2, a3, a4, a5, a6, i; a0:=1; a1:=0; a2:=0; a3:=0; a4:=0; a5:=0; a6:=0; print(a0); print(a1); print(a2); print(a3); print(a4); print(a5); print(a6); for i from 0 by 1 to n do a:=a0+a1; a0:=a1; a1:=a2; a2:=a3; a3:=a4; a4:=a5; a5:=a6; a6:=a; print(a); od; end: P(100); - Paolo P. Lava (ppl(AT)spl.at), Jun 28 2007
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CROSSREFS
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Sequence in context: A057094 A047998 A017847 this_sequence A091006 A167365 A025894
Adjacent sequences: A127838 A127839 A127840 this_sequence A127842 A127843 A127844
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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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