Search: id:A097924
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%I A097924
%S A097924 2,7,30,127,538,2279,9654,40895,173234,733831,3108558,13168063,55780810,
%T A097924 236291303,1000946022,4240075391,17961247586,76085065735,322301510526,
%U A097924 1365291107839,5783465941882,24499154875367,103780085443350
%N A097924 Sequence relates numerators and denominators in the continued fraction 
               convergents to sqrt(5).
%C A097924 a(n) = A001077(n+1) - 2*A001076(n).
%C A097924 A048875(n) + .5(A001077(n+1)) = .5(a(n)) + A048876(n).
%H A097924 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A097924 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A097924 a(n) = [(2sqrt(5)+3)*(2+sqrt(5))^n + (2sqrt(5)-3)*(2-sqrt(5))^n]/(2sqrt(5)).
%F A097924 a(n+1) = A001077(n+1) + A015448(n+2) - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), 
               Mar 08 2005
%F A097924 a(n)=4*a(n-1)+a(n-2), n>1 ; a(0)=2, a(1)=7 . G.f.: (2-x)/(1-4*x-x^2). 
               [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 20 2008]
%t A097924 a[n_] := Expand[((2Sqrt[5] + 3)*(2 + Sqrt[5])^n + (2Sqrt[5] - 3)*(2 - 
               Sqrt[5])^n)/(2Sqrt[5])]; Table[ a[n], {n, 0, 20}] (from Robert G. 
               Wilson v Sep 17 2004)
%o A097924 Floretion Algebra Multiplication Program, FAMP Code: 2lesforcycseq[ ( 
               - 'i + 'j - i' + j' - 'kk' - 'ik' - 'jk' - 'ki' - 'kj' )*( .5'i + 
               .5i' ) ], 2vesforcycseq = A000004. (Dement)
%Y A097924 Cf. A001077, A001076.
%Y A097924 Sequence in context: A042913 A041805 A074416 this_sequence A027136 A116363 
               A046648
%Y A097924 Adjacent sequences: A097921 A097922 A097923 this_sequence A097925 A097926 
               A097927
%K A097924 nonn
%O A097924 0,1
%A A097924 Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Sep 04 2004; 
               corrected Sep 16 2004
%E A097924 Edited, corrected and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Sep 17 2004

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