OFFSET
1,2
LINKS
Jukka Kohonen, Table of n, a(n) for n = 1..1000
J. Kohonen, Counting graded lattices of rank three that have few coatoms, arXiv:1804.03679 [math.CO] preprint (2018).
FORMULA
a(n) = (97/144)n^3 - (5/6)n^2 + [44/48, 47/48]n + [0, 13, 8, -45, 40, -19, 0, -5, 8, -27, 40, -37]/72. The value of the first bracket depends on whether n is even or odd. The value of the second bracket depends on whether (n mod 12) is 0, 1, 2, ..., 11.
Conjectures from Colin Barker, Dec 19 2018: (Start)
G.f.: x*(1 + 3*x + 8*x^2 + 17*x^3 + 21*x^4 + 21*x^5 + 16*x^6 + 7*x^7 + 3*x^8) / ((1 - x)^4*(1 + x)^2*(1 + x^2)*(1 + x + x^2)).
a(n) = a(n-1) + a(n-2) - 2*a(n-5) + a(n-8) + a(n-9) - a(n-10) for n>10.
(End)
EXAMPLE
a(2)=4: These are the four lattices.
__o__ __o__ __o__ __o__
/ / \ \ / / \ \ / / \ \ / / \ \
o o o o o o o o o o o o o o o o
\_\ /_/| \|/ \| \|/ | |/ \|
o o o o o o o o
\ / \ / \ / \_ _/
o o o o
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jukka Kohonen, Dec 19 2018
STATUS
approved