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A084134
a(n) = 8*a(n-1) - 6*a(n-2), a(0) = 1, a(1) = 4.
4
1, 4, 26, 184, 1316, 9424, 67496, 483424, 3462416, 24798784, 177615776, 1272133504, 9111373376, 65258185984, 467397247616, 3347628865024, 23976647434496, 171727406285824, 1229959365679616, 8809310487721984
OFFSET
0,2
COMMENTS
Binomial transform ofA005667.
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).
MATHEMATICA
LinearRecurrence[{8, -6}, {1, 4}, 30] (*Harvey P. Dale,Nov 30 2011 *)
PROG
(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
(SageMath)
A084134=BinaryRecurrenceSequence(8, -6, 1, 4)
[A084134(n) for n in range(41)] #G. C. Greubel,Oct 13 2022
KEYWORD
easy,nonn
AUTHOR
Paul Barry,May 16 2003
STATUS
approved