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A007075 Number of irreducible positions of size n in Montreal solitaire.
(Formerly M1441)
7
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: A024576 A057960 A227045 * A000107 A063028 A085810

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 February 19 18:31 EST 2018. Contains 299356 sequences. (Running on oeis4.)