cp's OEIS Frontend

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.

A022355 Fibonacci sequence beginning 0, 21.

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%I A022355 #21 Feb 20 2017 12:08:11
%S A022355 0,21,21,42,63,105,168,273,441,714,1155,1869,3024,4893,7917,12810,
%T A022355 20727,33537,54264,87801,142065,229866,371931,601797,973728,1575525,
%U A022355 2549253,4124778,6674031,10798809,17472840,28271649,45744489,74016138,119760627,193776765
%N A022355 Fibonacci sequence beginning 0, 21.
%H A022355 Colin Barker, <a href="/A022355/b022355.txt">Table of n, a(n) for n = 0..1000</a>
%H A022355 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A022355 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1).
%F A022355 G.f.: 21*x/(1 - x - x^2). - _Philippe Deléham_, Nov 20 2008
%F A022355 a(n) = 21*Fibonacci(n) = h*Fibonacci(n+k) + Fibonacci(n+k-h) with h=8, k=2. - _Bruno Berselli_, Feb 20 2017
%F A022355 From _Colin Barker_, Feb 20 2017: (Start)
%F A022355 a(n) = -21*(((1-sqrt(5))/2)^n - ((1+sqrt(5))/2)^n) / sqrt(5).
%F A022355 a(n) = a(n-1) + a(n-2) for n>1.
%F A022355 (End)
%t A022355 LinearRecurrence[{1, 1}, {0, 21}, 30] (* _Harvey P. Dale_, Dec 13 2014 *)
%o A022355 (PARI) concat(0, Vec(21*x/(1 - x - x^2) + O(x^50))) \\ _Colin Barker_, Feb 20 2017
%Y A022355 Cf. A000045.
%K A022355 nonn,easy
%O A022355 0,2
%A A022355 _N. J. A. Sloane_