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A240736 Number of compositions of n having exactly one fixed point. 3
1, 1, 1, 4, 7, 16, 29, 60, 120, 238, 479, 956, 1910, 3817, 7633, 15252, 30491, 60955, 121865, 243650, 487165, 974112, 1947851, 3895086, 7789153, 15576624, 31150481, 62296424, 124585395, 249158607, 498297297, 996562085, 1993071152, 3986055928, 7971971230 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

a(n) ~ c * 2^n, where c = A065442 * A048651 / 2 = 0.2319972162254452238942023675457837005318389885... - Vaclav Kotesovec, Sep 06 2014

EXAMPLE

a(4) = 4: 13, 22, 112, 1111.

a(5) = 7: 14, 32, 131, 221, 1112, 1121, 11111.

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, 2))

    end:

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

seq(a(n), n=1..40);

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, 2}]]; a[n_] := SeriesCoefficient[b[n, 1], {x, 0, 1}]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Nov 06 2014, after Maple *)

CROSSREFS

Column k=1 of A238349 and of A238350.

Sequence in context: A025619 A093210 A133600 * A286741 A298344 A285654

Adjacent sequences:  A240733 A240734 A240735 * A240737 A240738 A240739

KEYWORD

nonn

AUTHOR

Joerg Arndt and Alois P. Heinz, Apr 11 2014

STATUS

approved

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Last modified October 15 04:33 EDT 2019. Contains 328026 sequences. (Running on oeis4.)