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 A171871 Triangle read by rows: Distinct classifications of N elements containing exactly R binary partitions. 7
 1, 0, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 3, 3, 0, 0, 0, 3, 17, 6, 0, 0, 0, 1, 36, 74, 11, 0, 0, 0, 1, 60, 573, 358, 23, 0, 0, 0, 0, 56, 2802, 7311, 1631, 47, 0, 0, 0, 0, 50, 10087, 107938, 83170, 7563, 106, 0, 0, 0, 0, 27, 26512, 1186969, 3121840, 866657, 34751, 235, 0, 0, 0, 0, 19 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 COMMENTS Significance of triangle suggested by Franklin T. Adams-Watters on Dec 19 2009. Row N has N terms in this sequence. The triangle starts: 1; 0, 1; 0, 0, 1; 0, 0, 1, 2; 0, 0, 0, 3, 3; 0, 0, 0, 0, 3, 17, 6; 0, 0, 0, 0, 1, 36, 74, 11; Value is A000055(N) when R=N-1 (last term in each row). (Conjectured by Robert Munafo Dec 28 2009, then proved by Andrew Weimholt and Franklin T. Adams-Watters on Dec 29 2009) Value is 1 when N=2^R. Value is 1 when N=(2^R)-1. Value is R when R>2 and N=(2^R)-2. Value is A034198(R) when R>2 and N=(2^R)-3. Conjecture: In general, in each column, the last 2^(R-1) values are the same as the first 2^(N-1) values from the corresponding row of A039754. - Robert Munafo, Dec 30 2009 Value is 0 for all (N,R) for which N is greater than 2^R. Each term A(N,R) can be computed most efficiently by first enumerating all classifications in A(N-1,R) plus those in A(N-1,R-1), and then adding an additional type and/or partition to each. LINKS Table of n, a(n) for n=0..70. R. Munafo, Classifications of N Elements CROSSREFS Cf. Row sums are A005646, column sums are A171832. Cf. A039754. Last term in each row is A000055(N). Same triangle read by columns is A171872. Sequence in context: A212172 A275812 A280683 * A076260 A245527 A287871 Adjacent sequences: A171868 A171869 A171870 * A171872 A171873 A171874 KEYWORD nonn,tabl AUTHOR Robert Munafo, Jan 21 2010 STATUS approved

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Last modified June 24 00:02 EDT 2024. Contains 373661 sequences. (Running on oeis4.)