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A166552
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a(n) = 3*a(n-2) for n > 2; a(1) = 1; a(2) = 4.
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3
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1, 4, 3, 12, 9, 36, 27, 108, 81, 324, 243, 972, 729, 2916, 2187, 8748, 6561, 26244, 19683, 78732, 59049, 236196, 177147, 708588, 531441, 2125764, 1594323, 6377292, 4782969, 19131876, 14348907, 57395628, 43046721, 172186884, 129140163
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OFFSET
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1,2
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COMMENTS
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Second binomial transform is A054491. Fourth binomial transform is A153594.
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LINKS
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FORMULA
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a(n) = (7+(-1)^n)*3^(1/4*(2*n-5+(-1)^n))/2.
G.f.: x*(1+4*x)/(1-3*x^2).
a(n) = 3^floor((n-1)/2)*4^(1-n%2). - M. F. Hasler, Dec 03 2014
E.g.f.: (sqrt(3)*sinh(sqrt(3)*x) + 4*cosh(sqrt(3)*x) - 4)/3. - Ilya Gutkovskiy, May 17 2016
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MATHEMATICA
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LinearRecurrence[{0, 3}, {1, 4}, 50] (* G. C. Greubel, May 17 2016 *)
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PROG
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(Magma) [ n le 2 select 3*n-2 else 3*Self(n-2): n in [1..35] ];
(PARI) a(n)=3^(n\2)*(4/3)^!bittest(n, 0) \\ M. F. Hasler, Dec 03 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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