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A245789
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Rectangular array A read by upward antidiagonals: A(k,n) = (2^k-1)^n, n,k >= 1.
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1
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1, 1, 3, 1, 9, 7, 1, 27, 49, 15, 1, 81, 343, 225, 31, 1, 243, 2401, 3375, 961, 63, 1, 729, 16807, 50625, 29791, 3969, 127, 1, 2187, 117649, 759375, 923521, 250047, 16129, 255, 1, 6561, 823543, 11390625, 28629151, 15752961, 2048383, 65025, 511
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OFFSET
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1,3
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COMMENTS
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A(k,n) is the number of sequences (X_1, X_2, ..., X_k) of subsets of the set {1, 2, ..., n} such that intersect_{j=1..k} X_j = null.
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REFERENCES
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Richard P. Stanley, Enumerative Combinatorics, Cambridge University Press, Vol. 1, Second edition, 2012, p. 14 (Example 1.1.16).
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LINKS
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EXAMPLE
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Array A begins:
1 3 7 15 31 63
1 9 49 225 961 3969
1 27 343 3375 29791 250047
1 81 2401 50625 923521 15752961
1 243 16807 759375 28629151 992436543
1 729 117649 11390625 887503681 62523502209
1 2187 823543 170859375 27512614111 3938980639167
1 6561 5764801 2562890625 852891037441 248155780267521
1 19683 40353607 38443359375 26439622160671 15633814156853823
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MATHEMATICA
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(* Array *)
a[k_, n_] := (2^k - 1)^n; Grid[Table[a[k, n], {n, 12}, {k, 12}]]
(* Array antidiagonals flattened *)
Flatten[Table[(2^k - 1)^(n - k + 1), {n, 12}, {k, n}]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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