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%I #15 Sep 08 2022 08:45:47
%S 1,14,60,296,1424,6880,33216,160384,774400,3739136,18054144,87173120,
%T 420909056,2032328704,9812951040,47381118976,228776280064,
%U 1104629596160,5333623504896,25753012404224,124346543636480,600398224162816
%N a(n) = 4*a(n-1) + 4*a(n-2) for n > 1; a(0) = 1, a(1) = 14.
%C Binomial transform of A164539. Second binomial transform of A164675. Inverse binomial transform of A164541.
%H Vincenzo Librandi, <a href="/A164540/b164540.txt">Table of n, a(n) for n = 0..164</a>
%H Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, <a href="http://www.emis.de/journals/JIS/VOL18/Szczyrba/sz3.html">Analytic Representations of the n-anacci Constants and Generalizations Thereof</a>, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4, 4).
%F a(n) = 4*a(n-1) + 4*a(n-2) for n > 1; a(0) = 1, a(1) = 14.
%F G.f.: (1+10*x)/(1-4*x-4*x^2).
%F a(n) = ((1+3*sqrt(2))*(2+2*sqrt(2))^n + (1-3*sqrt(2))*(2-2*sqrt(2))^n)/2.
%o (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+3*r)*(2+2*r)^n+(1-3*r)*(2-2*r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Aug 20 2009
%Y Cf. A164539, A164675, A164541.
%K nonn,easy
%O 0,2
%A Al Hakanson (hawkuu(AT)gmail.com), Aug 15 2009
%E Edited and extended beyond a(5) by _Klaus Brockhaus_, Aug 20 2009
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