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%I #20 Jun 13 2015 00:51:29
%S 1,3,7,21,37,123,187,681,937,3663,4687,19341,23437,100803,117187,
%T 520401,585937,2667543,2929687,13599861,14648437,69047883,73242187,
%U 349433721,366210937,1763945823,1831054687,8886837981,9155273437,44702625363
%N Sum( k=0..n, C(floor((n+1)/2),floor((k+1)/2))*2^k ).
%H Vincenzo Librandi, <a href="/A097162/b097162.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,9,-9,-20,20)
%F G.f.: (1+2*x-5*x^2-4*x^3)/((1-x)*(1-4*x^2)*(1-5*x^2)).
%F a(n) = (3/4-3*sqrt(5)/4)*(-sqrt(5))^n +(3/4+3*sqrt(5)/4)*(sqrt(5))^n-(2^n-(-2)^n)-1/2.
%F a(2*n) = A057651(n); a(2*n+1)=3*A097165(n).
%F a(n+5) = 20*a(n)-20*a(n+1)-9*a(n+2)+9*a(n+3)+a(n+4). - _Robert Israel_, Sep 18 2014
%p A097162:=n->add(binomial(floor((n+1)/2),floor((k+1)/2))*2^k, k=0..n): seq(A097162(n), n=0..30); # _Wesley Ivan Hurt_, Sep 18 2014
%t LinearRecurrence[{1,9,-9,-20,20},{1,3,7,21,37},50] (* _Vincenzo Librandi_, Jan 30 2012 *)
%Y Cf. A075427.
%Y Cf. A057651, A097165.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Jul 30 2004
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