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, 3, 3] 6
[ 5] [0, 18, 12] 30
[ 6] [0, 4, 12, 4] 20
[ 7] [0, 40, 80, 20] 140
[ 8] [0, 5, 40, 20, 5] 70
[ 9] [0, 75, 375, 150, 30] 630
[10] [0, 6, 120, 90, 30, 6] 252
[11] [0, 126, 1470, 882, 252, 42] 2772
[12] [0, 7, 350, 371, 147, 42, 7] 924
T(6,3) = 4 because four orbitals over six sectors have a maximal up-run of length 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].
PROG
(Sage) # uses[unit_orbitals from A274709]
# Brute force counting
def orbital_ascent(n):
if n < 2: return [1]
S = [0]*((n+2)//2)
for u in unit_orbitals(n):
B = [0]*n
for i in (0..n-1):
B[i] = 0 if u[i] <= 0 else B[i-1] + u[i]
S[max(B)] += 1
return S
for n in (0..12): print(orbital_ascent(n))
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Peter Luschny, Jul 12 2016
STATUS
approved