A007046 Number of irreducible positions of size n in Montreal solitaire. (Formerly M2800)

1, 3, 9, 25, 70, 194, 537, 1485, 4104, 11338, 31318, 86498, 238885, 659713, 1821843, 5031071, 13893316, 38366206, 105947374, 292570493, 807923428, 2231050832, 6160961041, 17013250192, 46981405457, 129737238488, 358264064448, 989331456469

Offset

3,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=3..30.

C. Cannings, J. Haigh, Montreal solitaire, J. Combin. Theory Ser. A 60 (1992), no. 1, 50-66.

Formula

a(n) = d(n, 2) where d(n, k) = 0 if n < k*(k+1)/2, d(n, k) = 1 if n = k*(k+1)/2, and d(n, k) = d(n, k+1) + Sum_{r=1..k} binomial(k + 1, r) * d(n - k*(k+1)/2 + r*(r-1)/2, r) if n > k*(k+1)/2 [From Cannings and Haigh]. - Sean A. Irvine, Sep 25 2017

Crossrefs

Cf. A007048, A007049, A007050, A007075, A007076.

Sequence in context: A297590 A244934 A291594 * A211286 A211285 A333498

Adjacent sequences: A007043 A007044 A007045 * A007047 A007048 A007049

Keyword

nonn

Author

N. J. A. Sloane, Mira Bernstein

Extensions

More terms from Sean A. Irvine, Sep 25 2017

Status

approved