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A016121
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Number of sequences (a_1, a_2, ..., a_n) of length n with a_1 = 1 satisfying a_i <= a_{i+1} <= 2*a_i.
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17
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1, 2, 5, 17, 86, 698, 9551, 226592, 9471845, 705154187, 94285792211, 22807963405043, 10047909839840456, 8110620438438750647, 12062839548612627177590, 33226539134943667506533207, 170288915434579567358828997806, 1630770670148598007261992936663653
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OFFSET
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0,2
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COMMENTS
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Number of n X n binary symmetric matrices with rows, considered as binary numbers, in nondecreasing order. - R. H. Hardin, May 30 2008
Also, number of (n+1) X (n+1) binary symmetric matrices with zero main diagonal and rows, considered as binary numbers, in nondecreasing order. - Max Alekseyev, Feb 06 2022
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..50
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FORMULA
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a(n) = Sum_{k=0..n} A097712(n, k). - Paul D. Hanna, Aug 24 2004
Equals the binomial transform of A008934 (number of tournament sequences): a(n) = Sum_{k=0..n} C(n, k)*A008934(k). - Paul D. Hanna, Sep 18 2005
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MATHEMATICA
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T[n_, k_] := T[n, k] = If[n < 0 || k > n, 0, If[n == k, 1, If[k == 0, 1, T[n - 1, k] + Sum[T[n - 1, j] T[j, k - 1], {j, 0, n - 1}]]]];
a[n_] := Sum[T[n, k], {k, 0, n}];
a /@ Range[0, 20] (* Jean-François Alcover, Oct 02 2019 *)
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CROSSREFS
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Row sums of triangle A097712.
Cf. A008934, A060690, A089006, A351157, A351158, A351287, A351288.
Sequence in context: A162041 A162042 A162043 * A216519 A245108 A195137
Adjacent sequences: A016118 A016119 A016120 * A016122 A016123 A016124
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KEYWORD
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nonn
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AUTHOR
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Jeffrey Shallit
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STATUS
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approved
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