A240739 Number of compositions of n having exactly four fixed points.

1, 1, 3, 7, 16, 30, 70, 144, 299, 615, 1261, 2584, 5238, 10624, 21482, 43350, 87331, 175703, 353074, 708963, 1422445, 2852299, 5716668, 11453033, 22938117, 45928418, 91941762, 184021452, 368267172, 736898601, 1474388631, 2949737232, 5901032198, 11804591355

Offset

10,3

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 10..1000

Formula

a(n) ~ c * 2^n, where c = 0.00134325422292269761312514583911029332451787453007326095828843859220629510... . - Vaclav Kotesovec, Sep 07 2014

Example

a(12) = 3: 12315, 12342, 123411.
a(13) = 7: 12145, 12325, 12343, 123151, 123412, 123421, 1234111.
a(14) = 16: 11345, 12245, 12335, 12344, 121451, 123116, 123152, 123251, 123413, 123422, 123431, 1231511, 1234112, 1234121, 1234211, 12341111.

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, 5))
    end:
a:= n-> coeff(b(n, 1), x, 4):
seq(a(n), n=10..50);

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, 5}]]; a[n_] := SeriesCoefficient[b[n, 1], {x, 0, 4}]; Table[a[n], {n, 10, 50}] (* Jean-François Alcover, Nov 07 2014, after Maple *)

Crossrefs

Column k=4 of A238349 and of A238350.

Sequence in context: A110585 A184677 A224340 * A301117 A000412 A192964

Adjacent sequences: A240736 A240737 A240738 * A240740 A240741 A240742

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Apr 11 2014

Status

approved