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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
OFFSET
21,3
LINKS
Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 21..1000
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
Column k=6 of A238349 and of A238350.
Sequence in context: A133124 A104004 A101509 * A240742 A240743 A240744
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Apr 11 2014
STATUS
approved