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A111017 a(n) = (A102877(n+1) - A102877(n))/2. 2

%I

%S 0,1,2,7,20,61,180,543,1622,4873,14598,43815,131384,394213,1182456,

%T 3547551,10642110,31926873,95778990,287338599,862010924,2586037645,

%U 7758098316,23274309567,69822884886,209468698473,628405963974

%N a(n) = (A102877(n+1) - A102877(n))/2.

%C First differences of A102877, divided by 2.

%H Robert Israel, <a href="/A111017/b111017.txt">Table of n, a(n) for n = 0..2095</a>

%F From _Robert Israel_, Jun 30 2020: (Start)

%F a(2*n) = 2*a(2*n-1) + 3*a(2*n-2) - 2*a(n-2) for n >= 2.

%F a(2*n+1) = 2*a(2*n) + 3*a(2*n-1) for n >= 1.

%F G.f. g(z) = ((1/z - 1)*h(z) - 1/z)/2 where h(z) is the G.f. of A102877.

%F (3*z-1)*(z+1)*g(z) = 2*z^4*g(z^2)-z.

%F (End)

%p f:= proc(n) option remember;

%p if n::even then 2*procname(n-1)+3*procname(n-2)-2*procname(n/2-2)

%p else 2*procname(n-1)+3*procname(n-2)

%p fi

%p end proc:

%p f(0):= 0: f(1):= 1: f(2):= 2:

%p map(f, [$0..50]); # _Robert Israel_, Jun 30 2020

%t a[0] := 1; a[1] := 1; a[n_] := If[EvenQ[n], 3*a[n - 1], 3*a[n - 1] - 2*a[(n - 3)/2]]; Table[(a[i + 1] - a[i])/2, {i, 1, 50}] (* _Stefan Steinerberger_, May 22 2007 *)

%o (PARI) {m=27; v=vector(m+1); v[1]=1; v[2]=1; for(n=2, m, k=3*v[n]; if(n%2==1, k=k-2*v[(n-1)/2]); v[n+1]=k); w=vector(m, n, (v[n+1]-v[n])/2); print(w)} /* _Klaus Brockhaus_, May 20 2007 */

%Y Cf. A102877.

%K nonn

%O 0,3

%A _Paul Curtz_, May 17 2007

%E Edited and extended by _Klaus Brockhaus_ and _Stefan Steinerberger_, May 20 2007

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Last modified April 19 17:04 EDT 2021. Contains 343116 sequences. (Running on oeis4.)