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%I #19 Sep 05 2020 03:12:40
%S 1,9,113,1593,23137,338409,4957649,72655641,1064876737,15607654857,
%T 228758827313,3352883803641,49142725927201,720277760311209,
%U 10557006115168913,154732499817791193,2267891697076964737
%N a(0)=1, a(1)=9, a(n) = 18*a(n-1) - 49*a(n-2) for n > 1.
%C a(n)/a(n-1) tends to 9 + 4*sqrt(2) = 14.65685424... - _Klaus Brockhaus_, Sep 25 2009
%H Seiichi Manyama, <a href="/A165224/b165224.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-49).
%F G.f.: (1-9x)/(1-18x+49x^2);
%F e.g.f.: exp(9x)*cosh(4*sqrt(2)x);
%F a(n) = Sum_{k=0..n} 8^k*binomial(2n,2k) = Sum_{k=0..n} 8^k*A086645(n,k);
%F a(n) = 7^n*T(n,9/7) where T is the Chebyshev polynomial of the first kind;
%F a(n) = (1+sqrt(8))^(2n)/2 + (1-sqrt(8))^(2n)/2.
%F a(n) = ((9-4*sqrt(2))^n + (9+4*sqrt(2))^n)/2. - _Klaus Brockhaus_, Sep 25 2009
%t LinearRecurrence[{18,-49},{1,9},20] (* _Harvey P. Dale_, Sep 30 2016 *)
%Y Column k=8 of A333988.
%Y Cf. A081294, A001541, A090965, A083884, A099140, A099141, A099142, A026244.
%K easy,nonn
%O 0,2
%A _Philippe Deléham_, Sep 08 2009
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