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 A238351 Number of compositions p(1)+p(2)+...+p(k) = n such that for no part p(i) = i (compositions without fixed points). 25
 1, 0, 1, 2, 3, 6, 11, 22, 42, 82, 161, 316, 624, 1235, 2449, 4864, 9676, 19267, 38399, 76582, 152819, 305085, 609282, 1217140, 2431992, 4860306, 9714696, 19419870, 38824406, 77624110, 155208405, 310352615, 620601689, 1241036325, 2481803050, 4963170896 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Column k=0 of A238349 and of A238350. REFERENCES M. Archibald, A. Blecher and A. Knopfmacher, Fixed points in compositions and words, accepted by the Journal of Integer Sequences LINKS Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 0..1000 M. Archibald, A. Blecher, and A. Knopfmacher, Fixed Points in Compositions and Words, J. Int. Seq., Vol. 23 (2020), Article 20.11.1. FORMULA a(n) ~ c * 2^n, where c = A048651/2 = 0.14439404754330121... - Vaclav Kotesovec, May 01 2014 EXAMPLE The a(7) = 22 such compositions are: 01:  [ 2 1 1 1 1 1 ] 02:  [ 2 1 1 1 2 ] 03:  [ 2 1 1 2 1 ] 04:  [ 2 1 1 3 ] 05:  [ 2 1 2 1 1 ] 06:  [ 2 1 2 2 ] 07:  [ 2 1 4 ] 08:  [ 2 3 1 1 ] 09:  [ 2 3 2 ] 10:  [ 2 4 1 ] 11:  [ 2 5 ] 12:  [ 3 1 1 1 1 ] 13:  [ 3 1 1 2 ] 14:  [ 3 1 2 1 ] 15:  [ 3 3 1 ] 16:  [ 3 4 ] 17:  [ 4 1 1 1 ] 18:  [ 4 1 2 ] 19:  [ 4 3 ] 20:  [ 5 1 1 ] 21:  [ 6 1 ] 22:  [ 7 ] MAPLE b:= proc(n, i) option remember; `if`(n=0, 1,        add(`if`(i=j, 0, b(n-j, i+1)), j=1..n))     end: a:= n-> b(n, 1): seq(a(n), n=0..50); MATHEMATICA b[n_, i_] := b[n, i] = If[n == 0, 1, Sum[If[i == j, 0, b[n-j, i+1]], {j, 1, n}]]; a[n_] := b[n, 1]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Nov 06 2014, after Maple *) CROSSREFS Sequence in context: A036589 A251656 A123341 * A043328 A141072 A002083 Adjacent sequences:  A238348 A238349 A238350 * A238352 A238353 A238354 KEYWORD nonn AUTHOR Joerg Arndt and Alois P. Heinz, Feb 25 2014 STATUS approved

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Last modified August 19 20:38 EDT 2022. Contains 356231 sequences. (Running on oeis4.)