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%I #28 Sep 05 2020 03:12:36
%S 1,8,92,1184,15632,207488,2757056,36643328,487039232,6473467904,
%T 86042074112,1143628341248,15200538791936,202038000386048,
%U 2685388609667072,35692849740775424,474411605904392192
%N a(n) = 6^n * T(n, 4/3) where T is the Chebyshev polynomial of the first kind.
%C In general, r^n * T(n,(r+2)/r) has g.f. (1-(r+2)*x)/(1-2*(r+2)*x + r^2*x^2), e.g.f. exp((r+2)*x)*cosh(2*sqrt(r+1)*x), a(n) = Sum_{k=0..n} (r+1)^k*binomial(2n,2k) and a(n) = (1+sqrt(r+1))^(2*n)/2 + (1-sqrt(r+1))^(2*n)/2.
%H Seiichi Manyama, <a href="/A099142/b099142.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16,-36).
%F G.f.: (1-8*x)/(1-16*x+36*x^2);
%F E.g.f.: exp(8*x)*cosh(2*sqrt(7)*x).
%F a(n) = 6^n * T(n, 8/6) where T is the Chebyshev polynomial of the first kind.
%F a(n) = Sum_{k=0..n} 7^k * binomial(2n, 2k).
%F a(n) = (1+sqrt(7))^(2*n)/2 + (1-sqrt(7))^(2*n)/2.
%F a(0)=1, a(1)=8, a(n) = 16*a(n-1) - 36*a(n-2) for n > 1. - _Philippe Deléham_, Sep 08 2009
%t LinearRecurrence[{16,-36},{1,8},20] (* _Harvey P. Dale_, Mar 09 2018 *)
%o (PARI) a(n) = 6^n*polchebyshev(n, 1, 4/3); \\ _Michel Marcus_, Sep 08 2019
%Y Column k=7 of A333988.
%Y Cf. A001541, A081294, A083884, A090965, A099140, A099141.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Sep 30 2004
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