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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 (list; graph; refs; listen; history; text; internal format)
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 - (N-1)*x. Thus, (1 + (N-1)*x - (1 + (N-1)*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

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Last modified February 22 09:07 EST 2020. Contains 332133 sequences. (Running on oeis4.)