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 A007075 Number of irreducible positions of size n in Montreal solitaire. (Formerly M1441) 6
 1, 2, 5, 13, 35, 95, 260, 714, 1965, 5415, 14934, 41206, 113730, 313958, 866801, 2393315, 6608473, 18248017, 50389350, 139144906, 384237186, 1061044865, 2930013158, 8091077148, 22343115337, 61699480866, 170380367189, 470497972866 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is also the number of indecomposable permutations with exactly n inversions; there is one indecomposable permutation with no inversions. - David Bevan, Dec 19 2017 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS David Bevan, Table of n, a(n) for n = 1..1000 C. Cannings, J. Haigh, Montreal solitaire, J. Combin. Theory Ser. A 60 (1992), no. 1, 50-66. FORMULA a(n) = d(n, 1) where d(n, k) is defined in A007046. - Sean A. Irvine, Oct 06 2017 The ordinary generating function is f(1), where f(v) satisfies the functional equation f(v) = v*(1 + f(1 + x*v) - f(1)). The variable x marks inversions and v marks left-to-right minima. - David Bevan, Dec 19 2017 EXAMPLE a(3) = 5; five indecomposable permutations have three inversions: 321, 2341, 2413, 3142, 4123. - David Bevan, Dec 19 2017 MATHEMATICA r[1, 1]=1; r[_, 0]:=0; r[n_, k_]:=r[n, k]=Sum[r[n-k, j]Binomial[j+1, k], {j, k-1, (Sqrt[8(n-k)+1]-1)/2}]; a[n_]:=Sum[r[n, k], {k, (Sqrt[8n+1]-1)/2}]; Array[a, 20] (* David Bevan, Dec 19 2017 *) CROSSREFS Cf. A007046, A007048, A007049, A007050, A007076. Sequence in context: A057960 A339479 A227045 * A000107 A366088 A370841 Adjacent sequences: A007072 A007073 A007074 * A007076 A007077 A007078 KEYWORD nonn AUTHOR N. J. A. Sloane, Mira Bernstein EXTENSIONS More terms from Sean A. Irvine, Oct 06 2017 STATUS approved

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Last modified May 26 11:31 EDT 2024. Contains 372824 sequences. (Running on oeis4.)