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%I #17 Jan 02 2024 09:05:03
%S 1,5,24,114,540,2556,12096,57240,270864,1281744,6065280,28701216,
%T 135815616,642686400,3041224704,14391229824,68100030720,322252805376,
%U 1524916647936,7215983055360,34146398444544,161582492335104,764616563343360,3618204426049536
%N a(n) = 6*a(n-1) - 6*a(n-2).
%C Companion sequence = A030192 beginning (1, 6, 30, 144, 684,...).
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6, -6).
%F a(n) = 6*a(n-1) - 6*a(n-2); a(1) = 1, a(2) = 5.
%F Term (1,1) of M^n, where M = the 3x3 matrix [1,1,1; 1,2,1; 3,1,3].
%F O.g.f.: x(1-x)/(1-6x+6x^2). a(n)=A030192(n-1)-A030192(n-2). - _R. J. Mathar_, May 31 2008
%F a(n) = Sum_{1<=k<=n} A030523(n,k)*2^(k-1). - _Philippe Deléham_, Feb 19 2013
%e a(5) = 540 = 6*a(4) - 6*a(3) = 6*(114) - 6*24.
%e a(5) = 540 = term (1,1) of X^5.
%t LinearRecurrence[{6,-6},{1,5},30] (* _Harvey P. Dale_, Oct 01 2014 *)
%Y Cf. A030192, A030523.
%K nonn,easy
%O 1,2
%A _Gary W. Adamson_ and _Roger L. Bagula_, May 28 2008
%E More terms from _R. J. Mathar_, May 31 2008
%E More terms from _Harvey P. Dale_, Oct 01 2014
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