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%I #27 Sep 08 2022 08:45:00
%S 1,5,39,265,1871,13065,91519,640505,4483791,31386025,219703199,
%T 1537920345,10765446511,75358117385,527506838079,3692547833785,
%U 25847834902031,180934844183145,1266543909544159,8865807366284825,62060651565042351
%N a(n) = 5*a(n-1) + 14*a(n-2), a(0)=1, a(1)=5.
%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.
%D F. P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, March 2014; Preprint on ResearchGate.
%H G. C. Greubel, <a href="/A053573/b053573.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,14).
%F a(n) = (7^(n+1) - (-2)^(n+1))/9.
%F a(n) = 5*a(n-1) + 14*a(n-2), with a(0)=1, a(1)=5.
%F G.f.: 1/(1-5*x-14*x^2). - _Zerinvary Lajos_, Apr 24 2009
%F E.g.f.: (7*exp(7*x) - 2*exp(-2*x))/9. - _G. C. Greubel_, May 16 2019
%t LinearRecurrence[{5,14},{1,5},30] (* _Harvey P. Dale_, May 29 2017 *)
%o (Sage) [lucas_number1(n,5,-14) for n in range(1, 16)] # _Zerinvary Lajos_, Apr 24 2009
%o (PARI) a(n)=n++;(7^n -(-2)^n)/9 \\ _Charles R Greathouse IV_, Jun 11 2011
%o (Magma) [(7^(n+1) -(-2)^(n+1))/9: n in [0..30]]; // _G. C. Greubel_, May 16 2019
%o (GAP) List([0..30], n-> (7^(n+1) -(-2)^(n+1))/9) # _G. C. Greubel_, May 16 2019
%Y Cf. A090409 (binom. transf.)
%K easy,nonn
%O 0,2
%A _Barry E. Williams_, Jan 18 2000
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