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A048694 Generalized Pellian with second term equal to 7.

%I A048694 #30 Jun 13 2015 00:50:00
%S A048694 1,7,15,37,89,215,519,1253,3025,7303,17631,42565,102761,248087,598935,
%T A048694 1445957,3490849,8427655,20346159,49119973,118586105,286292183,
%U A048694 691170471,1668633125,4028436721,9725506567
%N A048694 Generalized Pellian with second term equal to 7.
%C A048694 Pisano period lengths: 1, 1, 8, 4, 12, 8, 6, 4, 24, 12, 24, 8, 28, 6, 24, 8, 16, 24, 40, 12, ... . - _R. J. Mathar_, Aug 10 2012
%H A048694 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A048694 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,1)
%F A048694 a(n) = ((6+sqrt(2))(1+sqrt(2))^n - (6-sqrt(2))(1-sqrt(2))^n)/2*sqrt(2).
%F A048694 a(n) = 2*a(n-1) + a(n-2); a(0)=1, a(1)=7.
%F A048694 G.f.: (1+5*x)/(1 - 2*x - x^2). - _Philippe Deléham_, Nov 03 2008
%F A048694 a(n) = ((1+sqrt(18))(1+sqrt(2))^n+(1-sqrt(18))(1-sqrt(2))^n)/2 offset 0. a(n) = first binomial transform of 1,6,2,12,4,24. - Al Hakanson (hawkuu(AT)gmail.com), Aug 01 2009
%p A048694 with(combinat): a:=n->5*fibonacci(n, 2)+fibonacci(n+1, 2): seq(a(n), n=0..26); # _Zerinvary Lajos_, Apr 04 2008
%t A048694 a[n_]:=(MatrixPower[{{1,2},{1,1}},n].{{6},{1}})[[2,1]]; Table[a[n],{n,0,40}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 20 2010 *)
%t A048694 LinearRecurrence[{2,1},{1,7},40] (* _Harvey P. Dale_, Jul 22 2011 *)
%o A048694 (Maxima)
%o A048694 a[0]:1$
%o A048694 a[1]:7$
%o A048694 a[n]:=2*a[n-1]+a[n-2]$
%o A048694 A048694(n):=a[n]$
%o A048694 makelist(A048694(n),n,0,30); /* _Martin Ettl_, Nov 03 2012 */
%Y A048694 Cf. A001333, A000129, A048654, A048655.
%K A048694 easy,nonn
%O A048694 0,2
%A A048694 _Barry E. Williams_