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%I #25 Dec 11 2019 06:59:18
%S 1,1,3,5,12,23,51,103,221,456,965,2009,4227,8833,18540,38803,81363,
%T 170399,357145,748176,1567849,3284833,6883059,14421533,30218028,
%U 63314735,132664227,277968871,582428789,1220356440,2557009709
%N Row sums of triangle A131321.
%C Equals INVERT transform of (1, 2, 0, 1, 0, 1, 0, 1, ...). - _Gary W. Adamson_, Apr 28 2009
%C The sequence is also the INVERT transform of the aerated odd-indexed Fibonacci numbers (i.e., of (1, 0, 2, 0, 5, 0, ...)). Sequence A124400 is the INVERT transform of the aerated even-indexed Fibonacci numbers. - _Gary W. Adamson_, Feb 07 2014
%F G.f.: (1-x^2)/(1 - x - 3x^2 + x^3 + x^4). - _Philippe Deléham_, Jan 21 2012
%F a(n) = a(n-1) + 3*a(n-2) - a(n-3) - a(n-4), a(0)=1, a(1)=1, a(2)=3, a(3)=5. - _Philippe Deléham_, Jan 21 2012
%F a(n) = Sum_{m=0..ceiling(n/2)} binomial(n-m,n-2*m)*Fibonacci(n-2*m+1). - _Vladimir Kruchinin_, Jan 26 2013
%e a(4) = 12 = 5 + 0 + 6 + 0 + 1.
%Y Cf. A131321, A000045.
%Y Cf. A124400.
%K nonn
%O 0,3
%A _Gary W. Adamson_, Jun 28 2007
%E a(10)-a(30) from _Philippe Deléham_, Jan 21 2012
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