|
|
A240741
|
|
Number of compositions of n having exactly six fixed points.
|
|
3
|
|
|
1, 1, 3, 7, 16, 35, 76, 155, 334, 691, 1427, 2928, 5985, 12181, 24718, 50052, 101060, 203767, 410240, 824943, 1657225, 3326530, 6672880, 13378262, 26809661, 53706442, 107555030, 215342201, 431063039, 862743300, 1726491928, 3454620480, 6911903675, 13828137410
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
21,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ c * 2^n, where c = 0.00000076865174785709491795394332754061911033555649913960925841174268897641... . - Vaclav Kotesovec, Sep 07 2014
|
|
MAPLE
|
b:= proc(n, i) option remember; `if`(n=0, 1, series(
add(b(n-j, i+1)*`if`(i=j, x, 1), j=1..n), x, 7))
end:
a:= n-> coeff(b(n, 1), x, 6):
seq(a(n), n=21..60);
|
|
MATHEMATICA
|
b[n_, i_] := b[n, i] = If[n == 0, 1, Series[Sum[b[n-j, i+1]*If[i == j, x, 1], {j, 1, n}], {x, 0, 7}]]; a[n_] := SeriesCoefficient[b[n, 1], {x, 0, 6}]; Table[a[n], {n, 21, 60}] (* Jean-François Alcover, Nov 07 2014, after Maple *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|