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A193641 Number of arrays of -1..1 integers x(1..n) with every x(i) in a subsequence of length 1 or 2 with sum zero. 8
1, 3, 7, 15, 33, 73, 161, 355, 783, 1727, 3809, 8401, 18529, 40867, 90135, 198799, 438465, 967065, 2132929, 4704323, 10375711, 22884351, 50473025, 111321761, 245527873, 541528771, 1194379303, 2634286479, 5810101729, 12814582761 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 1 of A193648.

Or yet empirical: row sums of triangle

m/k.|..0.....1.....2.....3.....4.....5.....6.....7

==================================================

.0..|..1

.1..|..1.....2

.2..|..1.....2.....4

.3..|..1.....2.....4.....8

.4..|..1.....4.....4.....8....16

.5..|..1.....4....12.....8....16....32

.6..|..1.....4....12....32....16....32....64

.7..|..1.....6....12....32....80....32....64...128

which is triangle for numbers 2^k*C(m,k) with triplicated diagonals. - Vladimir Shevelev, Apr 13 2012

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..200

Tomislav Doslic, I. Zubac, Counting maximal matchings in linear polymers, Ars Mathematica Contemporanea 11 (2016) 255-276.

FORMULA

Empirical: a(n) = 2*a(n-1) +a(n-3).

Empirical: G.f.: -x*(1+x+x^2) / ( -1+2*x+x^3 ). a(n) = A008998(n-3)+A008998(n-2)+A008998(n-1). - R. J. Mathar, Feb 19 2015

Empirical: a(n) = 1 + 2*A077852(n-2) for n >= 2. - Greg Dresden, Apr 04 2021

EXAMPLE

Some solutions for n=6

..1....1....1....0....0....1...-1....1....0...-1...-1....0....0....0...-1...-1

.-1...-1...-1....0...-1...-1....1...-1....1....1....1....1....1....0....1....1

.-1....0....1....0....1....1....0....0...-1...-1....0...-1...-1....1...-1....1

..1....1....1....0....1....0...-1...-1....1....1....0....0...-1...-1...-1...-1

..0...-1...-1...-1...-1....0....1....1...-1....0....0....0....1....1....1....1

..0....1....1....1....1....0...-1....0....0....0....0....0....0...-1...-1...-1

PROG

(Haskell)

a193641 n = a193641_list !! n

a193641_list = drop 2 xs where

   xs = 1 : 1 : 1 : zipWith (+) xs (map (* 2) $ drop 2 xs)

-- Reinhard Zumkeller, Jan 01 2014

CROSSREFS

Sequence in context: A079444 A269560 A146654 * A026701 A249512 A140498

Adjacent sequences:  A193638 A193639 A193640 * A193642 A193643 A193644

KEYWORD

nonn

AUTHOR

R. H. Hardin, Aug 02 2011

STATUS

approved

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Last modified September 19 00:22 EDT 2021. Contains 347549 sequences. (Running on oeis4.)