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Search: id:A127838
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| A127838 |
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a(1) = 1, a(2) = a(3) = a(4) = 0, a(n) = a(n-4)+a(n-3) for n>4. |
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| 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 2, 1, 1, 3, 3, 2, 4, 6, 5, 6, 10, 11, 11, 16, 21, 22, 27, 37, 43, 49, 64, 80, 92, 113, 144, 172, 205, 257, 316, 377, 462, 573, 693, 839, 1035, 1266, 1532, 1874, 2301, 2798, 3406, 4175, 5099, 6204, 7581
(list; graph; listen)
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OFFSET
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1,12
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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...4} (r_i^n)/(3(r_i)^2+4(r_i)) where r_i is a root of x^4=x+1
a(n)=A017817(n-5) for n>=5. O.g.f.: x(x-1)(1+x+x^2)/(x^4+x^3-1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 06 2008
O.g.f.: x*(x-1)*(x^2+x+1)/(-1+x^3+x^4). a(n)=A017817(n-5). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 09 2008
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MAPLE
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P:=proc(n) local a, a0, a1, a2, a3, a4, i; a0:=1; a1:=0; a2:=0; a3:=0; print(a0); print(a1); print(a2); print(a3); for i from 1 by 1 to n do a:=a0+a1; a0:=a1; a1:=a2; a2:=a3; a3:=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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Adjacent sequences: A127835 A127836 A127837 this_sequence A127839 A127840 A127841
Sequence in context: A099509 A131336 A052253 this_sequence A017817 A053268 A101417
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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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