%I #19 Oct 09 2024 07:38:10
%S 66,22335,7593834,2581881225,877832022666,298460305825215,
%T 101475626148550434,34501414430201322345,11730379430642301046866,
%U 3988294505003952154612095,1356008401321913090267065434,461038868154945446738647635465,156751859164280129978049928992666
%N Subsequence of A167708 whose indices are 2 mod 5.
%H Colin Barker, <a href="/A167778/b167778.txt">Table of n, a(n) for n = 0..394</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (340,-1).
%F a(n) = A167708(5n+2).
%F a(n+2) = 340*a(n+1) - a(n).
%F a(n+1) = 170*a(n) + 39*sqrt(19*a(n)^2-1539).
%F G.f.: (66 + 22335*x - 66*x*340)/(1 - 340*x + x^2).
%F a(n) = ((66 + 15*sqrt(19))/2)*(170 + 39*sqrt(19))^n + ((66 - 15*sqrt(19)) /2)*(170 - 39*sqrt(19))^n. - _Richard Choulet_, Nov 13 2009
%F G.f.: -3*(35*x - 22) / (x^2 - 340*x + 1). - _Colin Barker_, Nov 16 2015
%p u(0):=66:u(1):=22335:for n from 0 to 20 do u(n+2):=340*u(n+1)-u(n):od:seq(u(n),n=0..20); taylor(((66+22335*z-66*z*340)/(1-340*z+z^2)),z=0,20); for n from 0 to 20 do u(n):=simplify((15*sqrt(19)+66)/2*(170+39*sqrt(19))^(n)+(-15*sqrt(19)+66)/2*(170-39*sqrt(19))^(n)):od:seq(u(n),n=0..20);
%t LinearRecurrence[{340, -1}, {66, 22335}, 20] (* _Bruno Berselli_, Nov 17 2015 *)
%o (PARI) Vec(-3*(35*x-22)/(x^2-340*x+1) + O(x^20)) \\ _Colin Barker_, Nov 16 2015
%o (Magma) I:=[66,22335]; [n le 2 select I[n] else 340*Self(n-1)-Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 17 2015
%Y Cf. A167708, A167709, A167774, A167775, A167779, A167780. - _Richard Choulet_, Nov 11 2009
%K nonn,easy
%O 0,1
%A _Richard Choulet_, Nov 11 2009
%E Definition corrected by _Richard Choulet_, Nov 15 2009
%E Typo in title fixed by _Colin Barker_, Nov 16 2015