OFFSET
0,2
COMMENTS
It is related to the sequence A180998 by R. H. Hardin.
In other words, a(n) is the number of independent vertex sets in the graph with n^2 vertices of the double wedge shown in the example. Neighbors are just the nearest horizontal and vertical points. The corresponding sequence for a single wedge of height n is given by A180998(n+2). - Andrew Howroyd, Apr 28 2020
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..24
Konrad Engel, On the Fibonacci Number of an M x N Lattice, The Fibonacci Quarterly, 28 (1990), pp. 72-78.
Eric Weisstein's World of Mathematics, Independent Vertex Set
FORMULA
The sequence was generated from a product of binary rectangular matrices
S(i), where initial values are S(1)= (11) with A(1) = 1 1, and subsequent
1 0
values S(n+1) = (A(n)S(n)T ) where A(n+1)= A(n)S(n)T
S(n)0(n)
Then the vector vector product V(n)V(n)T (where T denotes transpose) gives the sequence where V(n)= S(1)S(2)......S(n). The sum of the elements of V(n) gives sequence A180998.
EXAMPLE
Single Wedge Lattice x Double Wedge Lattice x
x x x x x
x x x x x x x x
V(3)= 11 111 11111 = (5 4 3 5 4)
101 10110
11011
Double Wedge V(3)V(3)T = 91
Single Wedge Sum(54354) = 21
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger W. Haskell, Apr 03 2013
EXTENSIONS
a(0)=1 prepended, a(6) corrected and terms a(10) and beyond from Andrew Howroyd, Apr 28 2020
STATUS
approved