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A016029
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a(1) = a(2) = 1, a(2n + 1) = 2*a(2n) and a(2n) = 2*a(2n - 1) + (-1)^n.
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2
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1, 1, 2, 5, 10, 19, 38, 77, 154, 307, 614, 1229, 2458, 4915, 9830, 19661, 39322, 78643, 157286, 314573, 629146, 1258291, 2516582, 5033165, 10066330, 20132659, 40265318, 80530637, 161061274, 322122547, 644245094
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OFFSET
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1,3
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COMMENTS
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Row sums of Riordan array ((1+x^3)/(1-x^4),x/(1-x)); - Paul Barry, Oct 08 2007
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LINKS
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Table of n, a(n) for n=1..31.
Index entries for linear recurrences with constant coefficients, signature (2, -1, 2).
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FORMULA
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(1/10) {3*2^n + 3*(-1)^[n/2] - (-1)^[(n+1)/2]}. G.f.: x(1-x+x^2)/[(1-2x)(1+x^2)]. - Ralf Stephan, Jan 12 2005
a(n)=2a(n-1)-a(n-2)+2a(n-3). Sequence is identical to its half second differences from the second term. First differences: 0, 1, 3, 5, 9, 19, 39, ... = 0 before absolute values of A078066. Second differences: 1, 2, 2, 4, 10, 20, 38, ... = A100088. a(n)+a(n+2)=3*2^n, A007283;a(n)+a(n+6)=39*2^n. - Paul Curtz, Dec 18 2007
a(n)=[1/5+(1/10)*I]*I^n+(3/5)*2^n+[1/5-(1/10)*I]*(-I)^n, with n>=0 and I=sqrt(-1) - Paolo P. Lava, Jun 10 2008
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MATHEMATICA
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LinearRecurrence[{2, -1, 2}, {1, 1, 2}, 31] (* Ray Chandler, Sep 23 2015 *)
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CROSSREFS
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Sequence in context: A263366 A068035 A304973 * A018327 A285571 A000099
Adjacent sequences: A016026 A016027 A016028 * A016030 A016031 A016032
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v
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STATUS
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approved
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