A084134 - OEIS

%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