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.

A227725 T(n,k) = number of small equivalence classes of n-ary Boolean functions that contain 2^k functions.

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%I A227725 #15 Nov 02 2021 13:16:14
%S A227725 2,2,1,2,3,2,2,7,14,23,2,15,70,345,3904
%N A227725 T(n,k) = number of small equivalence classes of n-ary Boolean functions that contain 2^k functions.
%C A227725 Left diagonal (k=0) has only 2s. Two functions (contradiction and tautology) are always alone in their respective sec, regardless of arity.
%C A227725 Second diagonal (k=1) is 2^n-1 (A000225). These are the n-ary linear Boolean functions. Each sec contains a row of a binary Walsh matrix and its complement.
%C A227725 Right diagonal (k=n) is A051502, the numbers of small equivalence classes of n-ary functions, that contain the highest possible number of 2^n functions.
%H A227725 Tilman Piesk, <a href="http://en.wikiversity.org/wiki/Equivalence_classes_of_Boolean_functions#sec">Small equivalence classes of Boolean functions</a>
%H A227725 <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>
%e A227725 Triangle begins:              Row sums (A000231)
%e A227725             2                         2
%e A227725          2     1                      3
%e A227725       2     3     2                   7
%e A227725    2     7    14    23               46
%e A227725 2    15    70    345   3904        4336
%Y A227725 Cf. A000231, A051502, A000225, A227722.
%K A227725 nonn,tabl,more
%O A227725 0,1
%A A227725 _Tilman Piesk_, Jul 22 2013