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User:Tilman Piesk
From OeisWiki
I am a 1982 born mathematical autodidact interested in discrete mathematics.
I contribute to various Wikimedia projects under the name mate2code.
My native language is German, and I live in Leipzig.
This page shows some sequences I am interested in. My own ones have this background. A list of my sequences is here.
Contents 
Boolean functions
A001317( A089633 ) = A211344 Atomic Boolean functions
A227722, A227723 Smallest elements in equivalence classes of Boolean functions (sec, bec), the latter a subsequence of the former
A054724, A039754 number of secs, becs of nary Boolean functions by weight
A000231, A000616 number of secs, becs of nary Boolean functions, row sums of the two triangles above
A227725 (A227724) number of nary secs that contain 2^k functions (and the same only for half full functions)
Subgroups of nimber addition (sona)
A190939 sona interpreted as binary numbers (my first sequence, added on 20110524)
The 2binomial coefficients give their number by weight: A022166(n,k) is the number of sona of size 2^n with weight 2^k. A022166(4,0...4) = (1,15,35,15,1).
A006116(n) is the number of all sona of size 2^n. A006116(n) = 67.
A227963 sonasecs (entries are from A227722) The same secs in the same order as in A190939, but represented by the smallest among the numeric values of its functions, instead of the unique odd one
A198260 runs of ones, A227961 corresponding tabf
A227960 sonabecs (subsequence of A227723)
A076831(n,k) is the number of becs of sona of size 2^n with weight 2^k. A076831(4,0...4) = (1,4,6,4,1). Not to be confused with Pascal's triangle (A007318).
A076766(n) is the number of all becs of sona of size 2^n. A076766(4) = 16. Not to be confused with powers of two (A000079).
A227962 Permutations that assign complementary sonabecs to each other
A182176 number of all Boolean functions related to sona of size 2^n. A182176(4) = 307 different Boolean functions can be seen in these 67 sec matrices.
Combinatorics
A055089 Finite permutations in reverse colexicographic order (Row n shows relevant digits of the nth finite permutation.)
A195665 Bitpermutations of nonnegative integers
A000041(n) is the number of integer partitions of n
A194602 Integer partitions interpreted as binary numbers
A000110(n) is the number of partitions of an nset (Bell numbers)
A231428 Set partitions interpreted as binary numbers
A211362 (A211363) Inversion sets of finite permutations interpreted as binary numbers (and the corresponding permutation of the integers)
A059590(n)th finite permutations have inversion vectors (A007623) that look like n in binary. (Or 2*n when a useless zero is appended.)
A211362( A059590 ) = A211364 shows the corresponding inversion sets interpreted as binary numbers.
Rencontres numbers: A008290(n,k) among first n! finite permutations leave k elements unchanged. Left column (k=0) shows numbers of derangements (A000166).
Refined rencontres numbers: A181897(n,k) among the first n! finite permutations have cycle type k. (See refined r.n. under reflected r.n.)
A198380 Cycle type (i.e. integer partition) of nth finite permutation, represented by index number of A194602
A000629(N+) = 2,6,26,150,1082... Necklaces of partitions of n+1 labeled beads. Logically distinct strings of first order quantifiers with n variables.
A000670(N+) = 1,3,13, 75, 541... Ordered Bell numbers counting ordered set partitions (half of last sequence)
A019538(n,k) = k!*A008277(n,k) is the number of (nk)faces of the permutohedron of order n, and thus the number of ordered set partitions with n elements. (Row sums are the ordered Bell numbers.)
A083355(n) is the number of preferential arrangements (PA) of partitions of an nset.
A232598(n,k) is the number of PA with k blocks. A233357(n,k) is the number of PA with k levels.
A187783(m,n) is the number of permutations of a multiset that contains m times the elements of a nset.
A248814 is its column 6. A248827 shows the row sums.
Arrays of permutations
A211365 Odd evening, parted  A211366 Odd evening, alternating 
A211367 Chains of transpositions  A211368 Rows of transpositions 
A211369 Transpositions  A100630 Nested transpositions 
A211370 Circular shift to the right  A051683 Circular shift to the left 
Partition related number triangles
tabl triangles, columns match number of blocks:
 tabl triangles, columns match number of singletons:
 tabf triangles, columns match type:
 Row sums:

Walsh permutations
A002884 number of nbit Walsh permutations
A053601 number of compression vectors with different elements, so A053601(n) = A002884(n) / n!
A195467 (A197819) Array of Gray code permutation powers (mod 2)
A239303 Compression vectors of square roots of Gray * bitreversal
A239304 Permutations corresponding to graphs corresponding to A239303
Nimber multiplication and powers of 2
Mat(m,n) = List ( KeyMat(m,n) )
Compressed table of nimproducts (A051775)
A223537(m,n) = A223539( A223538(m,n) )
List
Table of nimproducts of powers of 2
A223541(m,n) = A223543( A223542(m,n) )
List
A223541 is symmetrical. Its lower triangle is A223540.
A002487(N+)=1, 1,2, 1,3,2,3, 1,4,3,5,2,5,3,4... Stern's diatomic series (probably the number of distinct entries in the antidiagonals of A223541)
Misc.
A000217(N+) = 1,3,6,10,15,21... Triangular numbers
A018900(N+) = 3, 5,6, 9,10,12, 17,18,20,24... Numbers that contain 2 binary ones
A001317(N0) = 1,3,5,15,17,51,85,255... Sierpinski triangle rows read like binary numbers
A197818(N0) = 1,3,5,15,17,51,93,255... Antidiagonals of the negated binary Walsh matrix read as binary numbers
A228539 (A228540) Rows of (negated) binary Walsh matrices read as binary numbers
Most entries in these two sequences are divisible by Fermat numbers (A000215).
A006046(2^n) = 3^n. Partial sum of Gould's sequence A001316.
A001222 (A001221) number of (distinct) prime factors of n
A001055 multiplicative partitions
And my 2 cents about lists with offset 0.
The array of positive integers
T(m,n) = m + (m+n2)(m+n1)/2
The rows, columns and diagonals of this array are important because they can be used to calculate the rows, columns and diagonals of other arrays.
The array  A000027  n  1,  2,  3,  4,  5,  6,  7,  8,  9,  10,  11,  12 
Main diagonal  A001844  2n^2 + 2n + 1  1,  5,  13,  25,  41,  61,  85,  113,  145,  181,  221,  265 
First knight moves diagonal  A064225  1,  8,  24,  49,  83,  126,  178,  239,  309,  388,  476,  573  
Second knight moves diagonal  A081267  ( 9n^2 + 7n + 2 ) / 2  1,  9,  26,  52,  87,  131,  184,  246,  317,  397,  486,  584 
col 1  A000217  ( n^2 + n ) / 2  1,  3,  6,  10,  15,  21,  28,  36,  45,  55,  66,  78 
col 2  A000096  ( n^2 + 3n ) / 2  2,  5,  9,  14,  20,  27,  35,  44,  54,  65,  77,  90 
Seqfan
 Infinite enumeration of finite partitions (20120202) Are there generally accepted orderings of all finite integer partitions or set partitions?
 Stern's diatomic series, nphitorial and the primes (20130410) The most numerous entries in the rows of Stern's diatomic series (A002487) all seem to be from A193339  and thus to be prime numbers.
 Definition of A211351
Sierpinski triangles in plots
Very incomplete list of sequences that somehow show a Sierpinski triangle in their scatterplot:
A117966/graph write n in ternary and then replace 2's with (1)'s
A227963/graph sonasecs
A080099/graph (n AND k), A080098/graph (n OR k), A051933/graph (n XOR k), A003987/graph (n XOR m, symmetric nimber addition table)
A223541/graph (A223540/graph, A223542/graph) nimproducts of powers of 2 (lower triangle, keymatrix)