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A016029 a(1) = a(2) = 1, a(2n + 1) = 2*a(2n) and a(2n) = 2*a(2n - 1) + (-1)^n. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row sums of Riordan array ((1+x^3)/(1-x^4),x/(1-x)); - Paul Barry, Oct 08 2007

LINKS

Table of n, a(n) for n=1..31.

Index entries for linear recurrences with constant coefficients, signature (2, -1, 2).

FORMULA

(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

MATHEMATICA

LinearRecurrence[{2, -1, 2}, {1, 1, 2}, 31] (* Ray Chandler, Sep 23 2015 *)

CROSSREFS

Sequence in context: A263366 A068035 A304973 * A018327 A285571 A000099

Adjacent sequences:  A016026 A016027 A016028 * A016030 A016031 A016032

KEYWORD

nonn

AUTHOR

Robert G. Wilson v

STATUS

approved

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Last modified November 20 05:07 EST 2019. Contains 329323 sequences. (Running on oeis4.)