

A007046


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


5



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
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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, 5066.


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*(r1)/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



