A084134 a(n) = 8*a(n-1) - 6*a(n-2), a(0) = 1, a(1) = 4.

1, 4, 26, 184, 1316, 9424, 67496, 483424, 3462416, 24798784, 177615776, 1272133504, 9111373376, 65258185984, 467397247616, 3347628865024, 23976647434496, 171727406285824, 1229959365679616, 8809310487721984

Offset: 0

Author

Paul Barry, May 16 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A005667.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-6).

Crossrefs

Cf. A005667, A084135.

Programs

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

Mathematica

LinearRecurrence[{8,-6},{1,4},30] (* Harvey P. Dale, Nov 30 2011 *)

SageMath

A084134=BinaryRecurrenceSequence(8,-6,1,4)
[A084134(n) for n in range(41)] # G. C. Greubel, Oct 13 2022

Formula

a(n) = (4+sqrt(10))^n/2 + (4-sqrt(10))^n/2.

G.f.: (1-4*x)/(1 - 8*x + 6*x^2).

E.g.f.: exp(4*x)*cosh(sqrt(10)*x).