

A259845


a(0)=1, a(1)=3, and the INVERT transform of the sequence deletes the 3.


1



1, 3, 4, 11, 38, 136, 512, 1993, 7958, 32420, 134216, 563030, 2388092, 10224320, 44127328, 191783029, 838623654, 3686965308, 16287624440, 72262899994, 321852273332, 1438540956048, 6450223722816, 29006443606746, 130790584554748, 591191800834696
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OFFSET

0,2


COMMENTS

The sequence is N = 3 in an infinite set, with the first few being:
A086581, N = 0: (1, 0, 1, 2, 5, 13, 35, 97,...)
A000108, N = 1: (1, 1, 2, 5, 14, 42, 132,...)
A171199, N = 2: (1, 2, 3, 8, 25, 83, 289,...)
... The INVERT transforms of the sequences delete the second terms in the sequences.
The g.f. was contributed by Paul D. Hanna: From the definition of the INVERT transform, 1/(1  x*A) = A  (N1)*x. Thus, (1 + (N1)*x  (1 + (N1)*x^2)*A) + x*A^2 = 0. The g.f. follows, below.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000


FORMULA

G.f.: A(x) = 1/(2*x) + x  sqrt(1  4*x  4*x^2 + 4*x^4)/(2*x).


EXAMPLE

The INVERT transform of (1, 3, 4, 11, 38, 136,...) is (1, 4, 11, 38, 136, ...).


CROSSREFS

Cf. A086581, A000108, A171199.
Sequence in context: A119042 A042273 A179167 * A037185 A299047 A296256
Adjacent sequences: A259842 A259843 A259844 * A259846 A259847 A259848


KEYWORD

nonn,eigen


AUTHOR

Gary W. Adamson, Jul 06 2015


EXTENSIONS

More terms from Alois P. Heinz, Jul 07 2015


STATUS

approved



