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 and 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
Empirical: partial sums of A052910. - Sean A. Irvine, Jul 14 2022
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 02 2011
STATUS
approved