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A084130
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a(n)=8a(n-1)-8a(n-2), a(0)=1,a(1)=4.
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5
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1, 4, 24, 160, 1088, 7424, 50688, 346112, 2363392, 16138240, 110198784, 752484352, 5138284544, 35086401536, 239584935936, 1635988275200, 11171226714112, 76281907511296, 520885446377472, 3556828310929408, 24287542916415488
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A001541.
(Start) Let U be the unit-primitive matrix (see [Jeffery])
U=U_(8,3)=
(0 0 0 1)
(0 0 2 0)
(0 2 0 1)
(2 0 2 0).
Then A084130(n)=(1/4)*Trace(U^(2*n)). (See also A006012, A001333.) - L. Edson Jeffery, April 4, 2011. (End)
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LINKS
| L. E. Jeffery, Unit-primitive matrices
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FORMULA
| a(n)=(4+sqrt(8))^n/2+(4-sqrt(8))^n/2; G.f.: (1-4x)/(1-8x+8x^2); E.g.f.: exp(4x)cosh(sqrt(8)x).
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PROG
| (PARI) {a(n)= if(n<0, 0, real((4+ 2*quadgen(8))^n))}
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CROSSREFS
| Cf. A084131.
Sequence in context: A091166 A078108 A117337 * A059304 A069722 A027079
Adjacent sequences: A084127 A084128 A084129 * A084131 A084132 A084133
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KEYWORD
| easy,nonn,changed
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 16 2003
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