cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A331509 Array read by antidiagonals: A(n,k) is the number of nonisomorphic T_0 n-regular set-systems on a k-set.

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%I A331509 #10 Feb 20 2022 11:32:39
%S A331509 1,1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,3,0,0,1,0,1,6,3,0,0,1,0,1,15,19,1,
%T A331509 0,0,1,0,1,42,141,29,0,0,0,1,0,1,109,1571,769,23,0,0,0,1,0,1,320
%N A331509 Array read by antidiagonals: A(n,k) is the number of nonisomorphic T_0 n-regular set-systems on a k-set.
%C A331509 An n-regular set-system is a finite set of nonempty sets in which each element appears in n blocks.
%C A331509 A set-system is T_0 if for every two distinct elements there exists a block containing one but not the other element.
%C A331509 A(n,k) is the number of nonequivalent binary matrices with k distinct columns and any number of distinct nonzero rows with n ones in every column up to permutation of rows and columns.
%e A331509 Array begins:
%e A331509 =================================
%e A331509 n\k | 0 1 2 3  4   5    6   7
%e A331509 ----+----------------------------
%e A331509   0 | 1 1 0 0  0   0    0   0 ...
%e A331509   1 | 1 1 1 1  1   1    1   1 ...
%e A331509   2 | 1 0 1 3  6  15   42 109 ...
%e A331509   3 | 1 0 0 3 19 141 1571 ...
%e A331509   4 | 1 0 0 1 29 769 ...
%e A331509   5 | 1 0 0 0 23 ...
%e A331509   ...
%e A331509 The A(2,3) = 3 matrices are:
%e A331509   [1 1 1]    [1 1 0]    [1 1 0]
%e A331509   [1 0 0]    [1 0 1]    [1 0 1]
%e A331509   [0 1 0]    [0 1 0]    [0 1 1]
%e A331509   [0 0 1]    [0 0 1]
%Y A331509 Row 2 appears to be A005368. Row 3 is A331716.
%Y A331509 Cf. A330942, A331039, A331461, A331508, A331510.
%K A331509 nonn,tabl,more
%O A331509 0,18
%A A331509 _Andrew Howroyd_, Jan 18 2020