OFFSET
0,4
COMMENTS
LINKS
Peter Luschny, Orbitals
EXAMPLE
Triangle read by rows, n>=0. The length of row n is floor((n+2)/2).
[ n] [k=0,1,2,...] [row sum]
[ 0] [1] 1
[ 1] [1] 1
[ 2] [0, 2] 2
[ 3] [0, 6] 6
[ 4] [0, 2, 4] 6
[ 5] [0, 10, 20] 30
[ 6] [0, 2, 12, 6] 20
[ 7] [0, 14, 84, 42] 140
[ 8] [0, 2, 28, 32, 8] 70
[ 9] [0, 18, 252, 288, 72] 630
[10] [0, 2, 60, 120, 60, 10] 252
T(6, 3) = 6 because the span of the following six orbitals is 3:
[-1, -1, -1, 1, 1, 1], [-1, -1, 1, 1, 1, -1], [-1, 1, 1, 1, -1, -1],
[1, -1, -1, -1, 1, 1], [1, 1, -1, -1, -1, 1], [1, 1, 1, -1, -1, -1].
PROG
(Sage) # uses[unit_orbitals from A274709]
from itertools import accumulate
# Brute force counting.
def orbital_span(n):
if n == 0: return [1]
S = [0]*((n+2)//2)
for u in unit_orbitals(n):
L = list(accumulate(u))
S[max(L) - min(L)] += 1
return S
for n in (0..10): print(orbital_span(n))
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Peter Luschny, Jul 10 2016
STATUS
approved