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%I #12 Oct 13 2022 17:32:12
%S 1,4,26,184,1316,9424,67496,483424,3462416,24798784,177615776,
%T 1272133504,9111373376,65258185984,467397247616,3347628865024,
%U 23976647434496,171727406285824,1229959365679616,8809310487721984
%N a(n) = 8*a(n-1) - 6*a(n-2), a(0) = 1, a(1) = 4.
%C Binomial transform of A005667.
%H G. C. Greubel, <a href="/A084134/b084134.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 (8,-6).
%F a(n) = (4+sqrt(10))^n/2 + (4-sqrt(10))^n/2.
%F G.f.: (1-4*x)/(1 - 8*x + 6*x^2).
%F E.g.f.: exp(4*x)*cosh(sqrt(10)*x).
%t LinearRecurrence[{8,-6},{1,4},30] (* _Harvey P. Dale_, Nov 30 2011 *)
%o (Magma) [n le 2 select 4^(n-1) else 8*Self(n-1) -6*Self(n-2): n in [1..40]]; // _G. C. Greubel_, Oct 13 2022
%o (SageMath)
%o A084134=BinaryRecurrenceSequence(8,-6,1,4)
%o [A084134(n) for n in range(41)] # _G. C. Greubel_, Oct 13 2022
%Y Cf. A005667, A084135.
%K easy,nonn
%O 0,2
%A _Paul Barry_, May 16 2003
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