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A127844
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a(1) = 1, a(2) = ... = a(10) = 0, a(n) = a(n-10)+a(n-9) for n>10.
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1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 0, 1, 4, 6, 4, 1, 0, 0, 0, 0, 1, 5, 10, 10, 5, 1, 0, 0, 0, 1, 6, 15, 20, 15, 6, 1, 0, 0, 1, 7, 21, 35, 35, 21, 7, 1, 0, 1, 8, 28
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,30
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COMMENTS
| 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
| S. Suter, Binet-like formulas for recurrent sequences with characteristic equation x^k=x+1, preprint, 2007
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FORMULA
| Binet-like formula: a(n)=sum_{i=1...10} (r_i^n)/(9(r_i)^2+10(r_i)) where r_i is a root of x^10=x+1
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MAPLE
| P:=proc(n)local a, a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, i; a0:=1; a1:=0; a2:=0; a3:=0; a4:=0; a5:=0; a6:=0; a7:=0; a8:=0; a9:=0; print(a0); print(a1); print(a2); print(a3); print(a4); print(a5); print(a6); print(a7); print(a8); print(a9); 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:=a7: a7:=a8; a8:=a9; a9:=a; print(a); od; end: P(100); - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 28 2007
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CROSSREFS
| Sequence in context: A181563 A056976 A124749 * A017877 A095683 A074079
Adjacent sequences: A127841 A127842 A127843 * A127845 A127846 A127847
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KEYWORD
| nonn
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AUTHOR
| Stephen Suter (sms5064(AT)psu.edu), Apr 02 2007
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