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.

A048695 Generalized Pellian with second term equal to 8.

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%I A048695 #25 Jun 13 2015 00:50:00
%S A048695 1,8,17,42,101,244,589,1422,3433,8288,20009,48306,116621,281548,
%T A048695 679717,1640982,3961681,9564344,23090369,55745082,134580533,324906148,
%U A048695 784392829,1893691806,4571776441,11037244688
%N A048695 Generalized Pellian with second term equal to 8.
%H A048695 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A048695 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,1)
%F A048695 a(n) = 2*a(n-1) + a(n-2); a(0)=1, a(1)=8.
%F A048695 a(n) = ((7+sqrt(2))(1+sqrt(2))^n - (7-sqrt(2))(1-sqrt(2))^n)/2*sqrt(2).
%F A048695 G.f.: (1+6*x)/(1 - 2*x - x^2). - _Philippe Deléham_, Nov 03 2008
%p A048695 with(combinat): a:=n->6*fibonacci(n-1,2)+fibonacci(n,2): seq(a(n), n=1..26); # _Zerinvary Lajos_, Apr 04 2008
%t A048695 a[n_]:=(MatrixPower[{{1,2},{1,1}},n].{{7},{1}})[[2,1]]; Table[a[n],{n,0,40}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 20 2010 *)
%t A048695 LinearRecurrence[{2,1},{1,8},30] (* _Harvey P. Dale_, May 01 2013 *)
%Y A048695 Cf. A001333, A000129, A048654, A048655.
%K A048695 easy,nonn
%O A048695 0,2
%A A048695 _Barry E. Williams_