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A163459 a(n) = 14*a(n-1) - 47*a(n-2) for n > 1; a(0) = 1, a(1) = 8.

%I A163459 #6 Sep 08 2022 08:45:46
%S A163459 1,8,65,534,4421,36796,307357,2573586,21584425,181223408,1522659737,
%T A163459 12799736142,107631298349,905250578212,7614837072565,64060941839946,
%U A163459 538955843348689,4534517540404184,38152320928270193,321010168596786054
%N A163459 a(n) = 14*a(n-1) - 47*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
%C A163459 Binomial transform of A163458. Inverse binomial transform of A163460.
%H A163459 G. C. Greubel, <a href="/A163459/b163459.txt">Table of n, a(n) for n = 0..1000</a>
%H A163459 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-47).
%F A163459 a(n) = ((2+sqrt(2))*(7+sqrt(2))^n + (2-sqrt(2))*(7-sqrt(2))^n)/4.
%F A163459 G.f.: (1-6*x)/(1-14*x+47*x^2).
%F A163459 E.g.f.: (1/2)*exp(7*x)*(sqrt(2)*sinh(sqrt(2)*x) + 2*cosh(sqrt(2)*x)). - _G. C. Greubel_, Dec 24 2016
%t A163459 LinearRecurrence[{14, -47}, {1, 8}, 50] (* _G. C. Greubel_, Dec 24 2016 *)
%o A163459 (Magma) [ n le 2 select 7*n-6 else 14*Self(n-1)-47*Self(n-2): n in [1..20] ];
%o A163459 (PARI) Vec((1-6*x)/(1-14*x+47*x^2) + O(x^50)) \\ _G. C. Greubel_, Dec 24 2016
%Y A163459 Cf. A163458, A163460.
%K A163459 nonn
%O A163459 0,2
%A A163459 _Klaus Brockhaus_, Jul 28 2009