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A240745
Number of compositions of n having exactly ten fixed points.
3
1, 1, 3, 7, 16, 35, 76, 162, 342, 715, 1484, 3049, 6266, 12788, 26017, 52773, 106791, 215654, 434766, 875271, 1760058, 3535850, 7097682, 14238236, 28546852, 57209494, 114608933, 229529157, 459567874, 919969090, 1841299703, 3684822059, 7373269689, 14752449235
OFFSET
55,3
LINKS
Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 55..1000
FORMULA
a(n) ~ c * 2^n, where c = 0.00000000000000004775074360891061857694419107988147903498648930287568336403... . - 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, 11))
end:
a:= n-> coeff(b(n, 1), x, 10):
seq(a(n), n=55..90);
MATHEMATICA
$RecursionLimit = 500; 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, 11}]]; a[n_] := SeriesCoefficient[b[n, 1], {x, 0, 10}]; Table[a[n], {n, 55, 90}] (* Jean-François Alcover, Nov 06 2014, after Maple *)
CROSSREFS
Column k=10 of A238349 and of A238350.
Sequence in context: A240742 A240743 A240744 * A227682 A099325 A026778
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Apr 11 2014
STATUS
approved