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A240738 Number of compositions of n having exactly three fixed points. 3
1, 1, 3, 7, 12, 30, 61, 126, 258, 537, 1083, 2205, 4465, 9023, 18192, 36612, 73633, 147893, 296818, 595313, 1193351, 2391121, 4789448, 9590503, 19199906, 38430421, 76910470, 153901337, 307932963, 616076971, 1232495756, 2465545205, 4931986957, 9865425657 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,3

LINKS

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 6..1000

FORMULA

a(n) ~ c * 2^n, where c = 0.01795631780689407343024911217251418606332716557572090051127381129853009022... . - Vaclav Kotesovec, Sep 07 2014

EXAMPLE

a(8) = 3: 1214, 1232, 12311.

a(9) = 7: 1134, 1224, 1233, 12141, 12312, 12321, 123111.

a(10) = 12: 11341, 12115, 12142, 12241, 12313, 12322, 12331, 121411, 123112, 123121, 123211, 1231111.

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, 4))

    end:

a:= n-> coeff(b(n, 1), x, 3):

seq(a(n), n=6..45);

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, 4}]]; a[n_] := SeriesCoefficient[b[n, 1], {x, 0, 3}]; Table[a[n], {n, 6, 45}] (* Jean-Fran├žois Alcover, Nov 07 2014, after Maple *)

CROSSREFS

Column k=3 of A238349 and of A238350.

Sequence in context: A063072 A007626 A193297 * A047068 A167490 A081533

Adjacent sequences:  A240735 A240736 A240737 * A240739 A240740 A240741

KEYWORD

nonn

AUTHOR

Joerg Arndt and Alois P. Heinz, Apr 11 2014

STATUS

approved

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Last modified February 24 16:02 EST 2020. Contains 332209 sequences. (Running on oeis4.)