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A154968
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a(n) = 4*a(n-1) + 12*a(n-2), n>2 with a(0)=1, a(1)=1, a(2)=7.
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2
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1, 1, 7, 40, 244, 1456, 8752, 52480, 314944, 1889536, 11337472, 68024320, 408146944, 2448879616, 14693281792, 88159682560, 528958111744, 3173748637696, 19042491891712, 114254951219200, 685529707577344
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OFFSET
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0,3
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LINKS
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FORMULA
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16*a(n) = 3*6^n +(-1)^n*2^n, n>0. - R. J. Mathar, Sep 03 2013
a(n) = (6^(n+1) - (-2)^(n+1))/32 + (3/4)*[n=0].
E.g.f.: (exp(-2*x) + 3*exp(6*x))/16. (End)
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MATHEMATICA
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LinearRecurrence[{4, 12}, {1, 1, 7}, 40] (* G. C. Greubel, Mar 01 2021 *)
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PROG
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(SageMath) [1]+[(6^(n+1) - (-2)^(n+1))/32 for n in [1..40]] # G. C. Greubel, Mar 01 2021
(Magma) [n eq 0 select 1 else (6^(n+1) -(-2)^(n+1))/32: n in [0..40]]; // G. C. Greubel, Mar 01 2021
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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