

A274878


A statistic on orbital systems over n sectors: the number of orbitals with span k.


10



1, 1, 0, 2, 0, 6, 0, 2, 4, 0, 10, 20, 0, 2, 12, 6, 0, 14, 84, 42, 0, 2, 28, 32, 8, 0, 18, 252, 288, 72, 0, 2, 60, 120, 60, 10, 0, 22, 660, 1320, 660, 110, 0, 2, 124, 390, 300, 96, 12, 0, 26, 1612, 5070, 3900, 1248, 156, 0, 2, 252, 1176, 1260, 588, 140, 14
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


COMMENTS

The definition of an orbital system is given in A232500 (see also the illustration there). The number of orbitals over n sectors is counted by the swinging factorial A056040.
The 'span' of an orbital w is the difference between the highest and the lowest
level of the orbital system touched by w.


LINKS

Table of n, a(n) for n=0..63.
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)
# Brute force counting, function unit_orbitals defined in A274709.
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

Cf. A056040 (row sum), A232500.
Other orbital statistics: A241477 (first zero crossing), A274706 (absolute integral), A274708 (number of peaks), A274709 (max. height), A274710 (number of turns), A274879 (returns), A274880 (restarts), A274881 (ascent).
Sequence in context: A322481 A262886 A138701 * A050821 A076257 A274881
Adjacent sequences: A274875 A274876 A274877 * A274879 A274880 A274881


KEYWORD

nonn,tabf


AUTHOR

Peter Luschny, Jul 10 2016


STATUS

approved



