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%I #25 Dec 10 2022 01:27:22
%S 1,0,6,6,42,78,330,798,2778,7566,24234,69630,215034,632814,1923018,
%T 5719902,17258010,51577422,155125482,464590014,1395342906,4182882990,
%U 12554940426,37652238366,112981880922,338895311118,1016786596650
%N a(n) = a(n-1) + 6*a(n-2), a(0)=1, a(1)=0.
%C Binomial transform is A102900.
%C Hankel transform is = 1,6,0,0,0,0,0,0,0,0,0,0,... - _Philippe Deléham_, Nov 02 2008
%D Maria Paola Bonacina and Nachum Dershowitz, Canonical Inference for Implicational Systems, in Automated Reasoning, Lecture Notes in Computer Science, Volume 5195/2008, Springer-Verlag.
%H Vincenzo Librandi, <a href="/A102901/b102901.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 (1,6).
%F G.f.: (1-x)/((1+2*x)*(1-3*x)).
%F a(n) = (2*3^n + 3*(-2)^n)/5.
%F a(n) = 6*A015441(n-1), for n>0.
%e a(6) = 330; (2*3^6 + 3*(-2)^6)/5 = (1458 + 192)/5 = 330.
%p A102901:=n->(2*3^n+3*(-2)^n)/5; seq(A102901(k), k=0..60); # _Wesley Ivan Hurt_, Nov 05 2013
%t CoefficientList[Series[(1-x)/((1+2x)(1-3x)), {x,0,50}], x] (* _Vincenzo Librandi_, Jul 20 2013 *)
%o (Magma) [(2*3^n+3*(-2)^n)/5: n in [0..50]]; // _Vincenzo Librandi_, Jul 20 2013
%o (PARI) a(n)=([0,1; 6,1]^n*[1;0])[1,1] \\ _Charles R Greathouse IV_, Mar 28 2016
%o (SageMath)
%o A102901=BinaryRecurrenceSequence(1,6,1,0)
%o [A102901(n) for n in range(51)] # _G. C. Greubel_, Dec 09 2022
%Y Cf. A015441, A102900.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Jan 17 2005
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