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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
OFFSET
3,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
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
KEYWORD
nonn
EXTENSIONS
More terms from Sean A. Irvine, Sep 25 2017
STATUS
approved