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A171475
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a(n) = 6*a(n-1) - 8*a(n-2), for n > 2, with a(0) = 1, a(1) = 6, a(2) = 27.
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1
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1, 6, 27, 114, 468, 1896, 7632, 30624, 122688, 491136, 1965312, 7862784, 31454208, 125822976, 503304192, 2013241344, 8053014528, 32212156416, 128848822272, 515395682304, 2061583515648, 8246335635456, 32985345687552
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = 3*(5*4^n - 2*2^n)/8 for n > 0.
G.f.: (1-x)*(1+x)/((1-2*x)*(1-4*x)).
E.g.f.: (1/8)*(-1 - 6*exp(2*x) + 15*exp(4*x)). - G. C. Greubel, Dec 02 2021
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MATHEMATICA
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Table[If[n==0, 1, 3*(5*4^n - 2*2^n)/8], {n, 0, 30}] (* G. C. Greubel, Dec 02 2021 *)
LinearRecurrence[{6, -8}, {1, 6, 27}, 30] (* Harvey P. Dale, Oct 25 2023 *)
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PROG
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(PARI) {m=21; v=concat([1, 6, 27], vector(m-3)); for(n=4, m, v[n]=6*v[n-1]-8*v[n-2]); v}
(Magma) I:=[6, 27]; [1] cat [n le 2 select I[n] else 6*Self(n-1) - 8*Self(n-2): n in [1..30]]; // G. C. Greubel, Dec 02 2021
(Sage) [1]+[3*(5*4^n - 2*2^n)/8 for n in (1..30)] # G. C. Greubel, Dec 02 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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