Search: id:A127839
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%I A127839
%S A127839 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,
%T A127839 16,13,22,35,36,29,35,57,71,65,64,92,128,136,129,156,220,264,265,285,
%U A127839 376,484,529,550,661,860,1013,1079,1211
%N A127839 a(1)=1,a(2)=...=a(5)=0,a(n)=a(n-5)+a(n-4) for n>5.
%C A127839 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.
%D A127839 S. Suter, Binet-like formulas for recurrent sequences with characteristic 
               equation x^k=x+1, preprint, 2007
%F A127839 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
%p A127839 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 (ppl(AT)spl.at), Jun 28 2007
%Y A127839 Sequence in context: A071919 A097805 A167763 this_sequence A017827 A094266 
               A071569
%Y A127839 Adjacent sequences: A127836 A127837 A127838 this_sequence A127840 A127841 
               A127842
%K A127839 nonn
%O A127839 1,15
%A A127839 Stephen Suter (sms5064(AT)psu.edu), Apr 02 2007

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