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%I #22 Feb 20 2022 15:12:55
%S 1,3,4,11,38,136,512,1993,7958,32420,134216,563030,2388092,10224320,
%T 44127328,191783029,838623654,3686965308,16287624440,72262899994,
%U 321852273332,1438540956048,6450223722816,29006443606746,130790584554748,591191800834696
%N a(0)=1, a(1)=3, and the INVERT transform of the sequence deletes the 3.
%C The sequence is N = 3 in an infinite set, with the first few being:
%C A086581, N = 0: (1, 0, 1, 2, 5, 13, 35, 97, ...)
%C A000108, N = 1: (1, 1, 2, 5, 14, 42, 132, ...)
%C A171199, N = 2: (1, 2, 3, 8, 25, 83, 289, ...)
%C ... The INVERT transforms of the sequences delete the second terms in the sequences.
%C The g.f. was contributed by _Paul D. Hanna_: From the definition of the INVERT transform, 1/(1 - x*A) = A - (N-1)*x. Thus, (1 + (N-1)*x - (1 + (N-1)*x^2)*A) + x*A^2 = 0. The g.f. follows, below.
%H Alois P. Heinz, <a href="/A259845/b259845.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: A(x) = 1/(2*x) + x - sqrt(1 - 4*x - 4*x^2 + 4*x^4)/(2*x).
%e The INVERT transform of (1, 3, 4, 11, 38, 136, ...) is (1, 4, 11, 38, 136, ...).
%Y Cf. A086581, A000108, A171199.
%K nonn,eigen
%O 0,2
%A _Gary W. Adamson_, Jul 06 2015
%E More terms from _Alois P. Heinz_, Jul 07 2015
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