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A176965
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a(n) = 2^(n-1) - (2^n*(-1)^n + 2)/3.
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3
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1, 0, 6, 2, 26, 10, 106, 42, 426, 170, 1706, 682, 6826, 2730, 27306, 10922, 109226, 43690, 436906, 174762, 1747626, 699050, 6990506, 2796202, 27962026, 11184810, 111848106, 44739242, 447392426, 178956970, 1789569706, 715827882, 7158278826
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OFFSET
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1,3
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COMMENTS
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The ratio a(n+1)/a(n) approaches 10 for even n and 2/5 for odd n as n->infinity.
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LINKS
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FORMULA
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a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3).
G.f.: x*(1 - x + 2*x^2)/( (1-x)*(1+2*x)*(1-2*x) ). (End)
a(n+2) = 4*a(n) + 2, a(1) = 1, a(2) = 0, n > 0. - Yosu Yurramendi, Mar 07 2017
a(n) = (-16 + (9 - (-1)^n) * 2^(n - (-1)^n))/24. - Loren M. Pearson, Dec 28 2019
E.g.f.: (3*exp(2*x) - 4*exp(x) + 3 - 2*exp(-2*x))/6. - G. C. Greubel, Dec 28 2019
a(n) = (2^n*5^(n mod 2) - 4)/6. - Heinz Ebert, Jun 29 2021
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MAPLE
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seq( (3*2^(n-1) -(-2)^n -2)/3, n=1..30); # G. C. Greubel, Dec 28 2019
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MATHEMATICA
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a[n_]:= a[n]= 2^(n-1)*If[n==1, 1, a[n-1]/2 +(-1)^(n-1)*Sqrt[(5 +4*(-1)^(n-1) )]/2]; Table[a[n], {n, 30}]
LinearRecurrence[{1, 4, -4}, {1, 0, 6}, 30] (* G. C. Greubel, Dec 28 2019 *)
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PROG
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(PARI) vector(30, n, (3*2^(n-1) -(-2)^n -2)/3 ) \\ G. C. Greubel, Dec 28 2019
(Magma) [(3*2^(n-1) -(-2)^n -2)/3: n in [1..30]]; // G. C. Greubel, Dec 28 2019
(Sage) [(3*2^(n-1) -(-2)^n -2)/3 for n in (1..30)] # G. C. Greubel, Dec 28 2019
(GAP) List([1..30], n-> (3*2^(n-1) -(-2)^n -2)/3); # G. C. Greubel, Dec 28 2019
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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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