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A127839
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a(1)=1,a(2)=...=a(5)=0,a(n)=a(n-5)+a(n-4) for n>5.
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1
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1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 1, 3, 3, 1, 1, 4, 6, 4, 2, 5, 10, 10, 6, 7, 15, 20, 16, 13, 22, 35, 36, 29, 35, 57, 71, 65, 64, 92, 128, 136, 129, 156, 220, 264, 265, 285, 376, 484, 529, 550, 661, 860, 1013, 1079, 1211
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OFFSET
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1,15
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COMMENTS
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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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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 1..1000
Index to sequences with linear recurrences with constant coefficients, signature (0,0,0,1,1)
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FORMULA
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Binet-like formula: a(n)=sum_{i=1...5} (r_i^n)/(4(r_i)^2+5(r_i)) where r_i is a root of x^5=x+1
G.f.: x*(x^4-1)/(x^5+x^4-1) [From Harvey P. Dale, Mar 19 2012]
a(n) = A017827(n-6) for n>=6. - R. J. Mathar, May 09 2013
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MAPLE
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P:=proc(n) local a, a0, a1, a2, a3, a4, a5, i; a0:=1; a1:=0; a2:=0; a3:=0; a4:=0; print(a0); print(a1); print(a2); print(a3); print(a4); for i from 1 by 1 to n do a:=a0+a1; a0:=a1; a1:=a2; a2:=a3; a3:=a4; a4:=a; print(a); od; end: P(100); - Paolo P. Lava, Jun 28 2007
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MATHEMATICA
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LinearRecurrence[{0, 0, 0, 1, 1}, {1, 0, 0, 0, 0}, 70] (* From Harvey P. Dale, Mar 19 2012 *)
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CROSSREFS
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Sequence in context: A071919 A097805 A167763 * A017827 A094266 A071569
Adjacent sequences: A127836 A127837 A127838 * A127840 A127841 A127842
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KEYWORD
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nonn,easy
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AUTHOR
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Stephen Suter (sms5064(AT)psu.edu), Apr 02 2007
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STATUS
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approved
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