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Search: id:A045649
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| A045649 |
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Number of chiral n-ominoes in n-1 space. |
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+0
3
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| 1, 0, 0, 1, 1, 1, 2, 5, 9, 15, 31, 70, 146, 300, 656, 1471, 3258, 7245, 16400, 37461, 85773, 197365, 457297, 1065070, 2489750, 5842741, 13766775, 32552087, 77208432, 183670145, 438176307, 1048092760, 2513081101
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OFFSET
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1,7
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COMMENT
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Lunnon's DR(n,n-1)-DE(n,n-1). Knuth describes methodology for a similar enumeration, that of free trees with n nodes.
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REFERENCES
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W. F. Lunnon, Counting Multidimensional Polyominoes, Computer Journal, Vol. 18 (1975), pp. 366-67.
D. E. Knuth, Fundamental Algorithms, 3d Ed. 1997, pp. 386-88.
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FORMULA
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G.f.: C(x)-C^2(x)/2+C(-x^2)/2 where C(x) is g.f. for same sequence with one cell labeled, A045648.
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MATHEMATICA
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s[ n_, k_ ] := s[ n, k ]=c[ n+1-k ]+If[ n<2k, 0, s[ n-k, k ](-1)^k ]; c[ 1 ]=1; c[ n_ ] := c[ n ]=Sum[ c[ i ]s[ n-1, i ]i, {i, 1, n-1} ]/(n-1); Table[ c[ i ]-Sum[ c[ j ]c[ i-j ], {j, 1, i/2} ]+If[ OddQ[ i ], 0, c[ i/2 ](c[ i/2 ]+(-1)^(i/2))/2 ], {i, 1, 33} ]
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CROSSREFS
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Cf. A045648, A000081, A004111.
Adjacent sequences: A045646 A045647 A045648 this_sequence A045650 A045651 A045652
Sequence in context: A007176 A065618 A054253 this_sequence A024519 A072829 A138226
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Robert A. Russell (russell(AT)post.harvard.edu)
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