OFFSET
0,13
COMMENTS
See Merris and Watkins (1983) for precise definition.
LINKS
Russell Merris and William Watkins, Tensors and graphs, SIAM J. Algebraic Discrete Methods 4 (1983), no. 4, 534-547.
Andrey Zabolotskiy, a259976 (implementation in Rust).
FORMULA
From Andrey Zabolotskiy, Aug 28 2018: (Start)
T(n,k) = A005368(k) for n >= 2*k. (End)
EXAMPLE
The triangle begins:
[0] 1
[1] 1
[2] 1
[3] 1,0,
[4] 1,0,1,1,
[5] 1,0,1,2,2,0,
[6] 1,0,1,3,4,6,6,3,
[7] 1,0,1,3,5,11,20,24,32,34,17
[8] 1,0,1,3,6,13,32,59,106,181,261,317,332,245,89
[9] 1,0,1,3,6,14,38,85,197,426,866,1615,2743,4125,5495,6318,6054,4416,1637
...
PROG
(Sage)
from sage.groups.perm_gps.permgroup_element import make_permgroup_element
for p in range(8):
m = p*(p-1)//2
Sm = SymmetricGroup(m)
denom = factorial(p)
elements = []
for perm in SymmetricGroup(p):
t = perm.tuple()
eperm = []
for v2 in range(p):
for v1 in range(v2):
w1, w2 = sorted([t[v1], t[v2]])
eperm.append((w2-1)*(w2-2)//2+w1)
elements.append(make_permgroup_element(Sm, eperm))
for q in range(m//2+1):
char = SymmetricGroupRepresentation([m-q, q]).to_character()
numer = sum(char(e) for e in elements)
print((p, q), numer//denom)
# Andrey Zabolotskiy, Aug 28 2018
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Jul 12 2015
EXTENSIONS
Name edited, terms T(7, 9)-T(7, 10) and rows 0-2, 8, 9 added by Andrey Zabolotskiy, Sep 06 2018
STATUS
approved