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A163416 a(n) = 20*a(n-1) - 98*a(n-2) for n>1, a(0)=1, a(1)=14.

%I A163416 #17 Sep 08 2022 08:45:46
%S A163416 1,14,182,2268,27524,328216,3866968,45174192,524520976,6063348704,
%T A163416 69863918432,803070195648,9214739906624,105593918958976,
%U A163416 1208833868330368,13828473308627712,158103747076178176,1806884557278047744,20643523932095493632,235795792028661193728,2692850495227865498624
%N A163416 a(n) = 20*a(n-1) - 98*a(n-2) for n>1, a(0)=1, a(1)=14.
%C A163416 Binomial transform of A163415. Tenth binomial transform of A143095.
%H A163416 G. C. Greubel, <a href="/A163416/b163416.txt">Table of n, a(n) for n = 0..940</a>
%H A163416 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20, -98).
%F A163416 a(n) = ((1 + 2*sqrt(2))*(10 + sqrt(2))^n + (1 - 2*sqrt(2))*(10 - sqrt(2))^n)/2.
%F A163416 O.g.f.: (1 - 6*x)/(1 - 20*x + 98*x^2).
%F A163416 E.g.f.: exp(10*x)*( cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - _G. C. Greubel_, Dec 21 2016
%t A163416 LinearRecurrence[{20,-98},{1,14},30] (* _Harvey P. Dale_, Aug 14 2012 *)
%o A163416 (Magma) [n le 2 select 13*n-12 else 20*Self(n-1)-98*Self(n-2): n in [1..17]];
%o A163416 (PARI) Vec((1-6*x)/(1-20*x+98*x^2) + O(x^50)) \\ _G. C. Greubel_, Dec 21 2016
%Y A163416 Cf. A163415, A143095.
%K A163416 nonn,easy
%O A163416 0,2
%A A163416 _Klaus Brockhaus_, Jul 27 2009