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 A099141 a(n) = 5^n * T(n,7/5) where T is the Chebyshev polynomial of the first kind. 7
 1, 7, 73, 847, 10033, 119287, 1419193, 16886527, 200931553, 2390878567, 28449011113, 338514191407, 4027973401873, 47928772841047, 570303484727833, 6786029465163487, 80746825394092993, 960804818888214727 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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(2*n,2*k) and a(n) = (1+sqrt(r+1))^(2*n)/2 + (1-sqrt(r+1))^(2*n)/2. LINKS Seiichi Manyama, Table of n, a(n) for n = 0..500 Index entries for linear recurrences with constant coefficients, signature (14,-25). FORMULA G.f.: (1-7*x)/(1-14*x+25*x^2); e.g.f.: exp(7*x)*cosh(2*sqrt(6)*x); a(n) = 5^n * T(n, 7/5) where T is the Chebyshev polynomial of the first kind; a(n) = Sum_{k=0..n} 6^k * binomial(2n, 2k); a(n) = (1+sqrt(6))^(2n)/2 + (1-sqrt(6))^(2n)/2. a(0)=1, a(1)=7, a(n) = 14*a(n-1) - 25*a(n-2) for n > 1. - Philippe Deléham, Sep 08 2009 MATHEMATICA LinearRecurrence[{14, -25}, {1, 7}, 30] (* Harvey P. Dale, Dec 26 2014 *) CROSSREFS Column k=6 of A333988. Cf. A081294, A001541, A090965, A083884, A099140, A099142. Sequence in context: A121127 A071060 A092444 * A084768 A106651 A114429 Adjacent sequences:  A099138 A099139 A099140 * A099142 A099143 A099144 KEYWORD easy,nonn AUTHOR Paul Barry, Sep 30 2004 STATUS approved

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Last modified July 27 02:39 EDT 2021. Contains 346302 sequences. (Running on oeis4.)