This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A127839 #22 Apr 24 2025 10:46:43
%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,
%T A127839 20,16,13,22,35,36,29,35,57,71,65,64,92,128,136,129,156,220,264,265,
%U A127839 285,376,484,529,550,661,860,1013,1079,1211
%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
%H A127839 Harvey P. Dale, <a href="/A127839/b127839.txt">Table of n, a(n) for n = 1..1000</a>
%H A127839 Sadjia Abbad and Hacène Belbachir, <a href="https://math.colgate.edu/~integers/z38/z38.pdf">The r-Fibonacci polynomial and its companion sequences linked with some classical sequences</a>, Integers (2025), Vol. 25, Art. No. A38. See p. 17.
%H A127839 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1,1)
%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.
%F A127839 G.f.: x*(x^4-1)/(x^5+x^4-1). - _Harvey P. Dale_, Mar 19 2012
%F A127839 a(n) = A017827(n-6) for n >= 6. - _R. J. Mathar_, May 09 2013
%t A127839 LinearRecurrence[{0,0,0,1,1},{1,0,0,0,0},70] (* _Harvey P. Dale_, Mar 19 2012 *)
%K A127839 nonn,easy
%O A127839 1,15
%A A127839 Stephen Suter (sms5064(AT)psu.edu), Apr 02 2007