OFFSET
0,4
COMMENTS
LINKS
Peter Luschny, Orbitals
EXAMPLE
The length of row n is 1+floor(n^2//4).
The triangle begins:
[n] [k=0,1,2,...] [row sum]
[0] [1] 1
[1] [1] 1
[2] [0, 2] 2
[3] [0, 4, 2] 6
[4] [2, 0, 2, 0, 2] 6
[5] [6, 4, 6, 4, 4, 4, 2] 30
[6] [0, 6, 0, 6, 0, 4, 0, 2, 0, 2] 20
[7] [6, 24, 16, 20, 14, 16, 12, 8, 6, 8, 4, 4, 2] 140
[8] [8, 0, 14, 0, 14, 0, 10, 0, 10, 0, 6, 0, 4, 0, 2, 0, 2] 70
T(5, 4) = 4 because the integral of four orbitals have the absolute value 4:
Integral([-1, -1, 1, 1, 0]) = -4, Integral([0, -1, -1, 1, 1]) = -4,
Integral([0, 1, 1, -1, -1]) = 4, Integral([1, 1, -1, -1, 0]) = 4.
PROG
# Brute force counting, function unit_orbitals defined in A274709.
def orbital_integral(n):
if n == 0: return [1]
S = [0]*(1+floor(n^2//4))
for u in unit_orbitals(n):
L = list(accumulate(accumulate(u)))
S[abs(L[-1])] += 1
return S
for n in (0..8): print orbital_integral(n)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Peter Luschny, Jul 10 2016
STATUS
approved