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A127839 a(1)=1, a(2)=...=a(5)=0, a(n) = a(n-5) + a(n-4) for n > 5. 1

%I #18 Feb 26 2024 01:58:50

%S 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,

%T 20,16,13,22,35,36,29,35,57,71,65,64,92,128,136,129,156,220,264,265,

%U 285,376,484,529,550,661,860,1013,1079,1211

%N a(1)=1, a(2)=...=a(5)=0, a(n) = a(n-5) + a(n-4) for n > 5.

%C 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 S. Suter, Binet-like formulas for recurrent sequences with characteristic equation x^k=x+1, preprint, 2007

%H Harvey P. Dale, <a href="/A127839/b127839.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1,1)

%F 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.

%F G.f.: x*(x^4-1)/(x^5+x^4-1). - _Harvey P. Dale_, Mar 19 2012

%F a(n) = A017827(n-6) for n >= 6. - _R. J. Mathar_, May 09 2013

%t LinearRecurrence[{0,0,0,1,1},{1,0,0,0,0},70] (* _Harvey P. Dale_, Mar 19 2012 *)

%K nonn,easy

%O 1,15

%A Stephen Suter (sms5064(AT)psu.edu), Apr 02 2007

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Last modified March 19 02:49 EDT 2024. Contains 370952 sequences. (Running on oeis4.)