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# User:Tilman Piesk/list

## legend

### seq

smi: the sequence is strictly monotonically increasing
smi,rows or smd,rows: the rows are strictly monotonically increasing or decreasing
mi: the sequence is monotonically increasing
mi,rows or md,rows: the rows are monotonically increasing or decreasing
perm: the sequence is a permutation of the integers
perm,rows: the rows are permutations of the first integers
sym,rows: the rows of the triangle or diagonals of the array are symmetric

### triangle

tabl,t: regular triangle, the n in T(n,k) stands for an antidiagonal of length n or n+1
tabl,a: array or matrix, the m in T(m,n) stands for an infinite horizontal row
when both interpretations make sense it's just tabl

tablf: the interpretation as tabl makes sense, but it is saved as a tabf (the rest of each row can be deduced from the beginning)

tabf(seq): length of row n is seq(n)

tabf(diff(seq)),view: actually just a sequence, but one that naturally divides into subsequences of length seq(n)
diff(seq) is the sequence of differences between consecutive elements of seq, e.g. diff(A000041) = A002865.

## list

date A seq triangle title
1 2011-05-24 A190939 smi tabf(diff(A006116)),view Subgroups of nimber addition interpreted as binary numbers.
2 2011-08-30 A194602 smi tabf(diff(A000041)),view Integer partitions interpreted as binary numbers.
3 2011-09-22 A195663 perm,rows tabl,a Array read by antidiagonals: Consecutive finite permutations of positive integers in reverse colexicographic order.
4 2011-09-22 A195664 perm,rows tabl,a Array read by antidiagonals: Consecutive finite permutations of non-negative integers in reverse colexicographic order.
5 2011-09-23 A195665 perm,rows tablf Consecutive bit-permutations of non-negative integers.
6 2011-10-18 A197818 smi tabf(diff(A000079)),view Walsh matrix antidiagonals converted to decimal.
7 2011-10-18 A197819 perm,rows tabf(A001146) Table of binary Walsh functions w(A001317), columns read as binary numbers.
8 2011-10-22 A198260 Runs of 1s in binary strings corresponding to subgroups of nimber addition.
9 2011-10-23 A198380 tabf(diff(A000142)),view Cycle type of the n-th finite permutation represented by index number of A194602.
10 2012-03-10 A209612 sym,rows tabl,t Triangle read by rows: T(n,k) is the number of k-block noncrossing partitions of n-set up to rotations and reflections.
11 2012-03-13 A209805 sym,rows tabl,t Triangle read by rows: T(n,k) is the number of k-block noncrossing partitions of n-set up to rotations.
12 2012-03-31 A181897 tabf(A000041) Triangle of refined rencontres numbers: T(n,k) is the number of permutations of n elements with cycle type k (k-th integer partition, defined by A194602).
13 2012-04-09 A211350 tabf(A000041) Refined triangle A124323: T(n,k) is the number of partitions of an n-set that are of type k (k-th integer partition, defined by A194602).
14 2012-04-09 A211351 tabf(A000041) Refined triangle A091867: T(n,k) is the number of noncrossing partitions of an n-set that are of type k (k-th integer partition, defined by A194602).
15 2012-04-09 A211352 tabf(A000041) Refined triangle A211356: T(n,k) is the number of partitions up to rotation of an n-set that are of type k (k-th integer partition, defined by A194602).
16 2012-04-09 A211353 tabf(A000041) Refined triangle A211357: T(n,k) is the number of noncrossing partitions up to rotation of an n-set that are of type k (k-th integer partition, defined by A194602).
17 2012-04-09 A211354 tabf(A000041) Refined triangle A211358: T(n,k) is the number of partitions up to rotation and reflection of an n-set that are of type k (k-th integer partition, defined by A194602).
18 2012-04-09 A211355 tabf(A000041) Refined triangle A211359: T(n,k) is the number of noncrossing partitions up to rotation and reflection of an n-set that are of type k (k-th integer partition, defined by A194602).
19 2012-04-12 A211356 tabl,t Triangle read by rows: T(n,k) is the number of partitions up to rotation of an n-set that contain k singleton blocks.
20 2012-04-12 A211357 tabl,t Triangle read by rows: T(n,k) is the number of noncrossing partitions up to rotation of an n-set that contain k singleton blocks.
21 2012-04-12 A211358 tabl,t Triangle read by rows: T(n,k) is the number of partitions up to rotation and reflection of an n-set that contain k singleton blocks.
22 2012-04-12 A211359 tabl,t Triangle read by rows: T(n,k) is the number of noncrossing partitions up to rotation and reflection of an n-set that contain k singleton blocks.
23 2012-04-12 A211360 Top elements of triangle A211350.
24 2012-04-12 A211361 Top elements of triangle A211351.
25 2012-06-03 A211362 tabf(diff(A000142)),view Inversion sets of finite permutations interpreted as binary numbers.
26 2012-06-03 A211363 perm tabf(diff(A000142)),view Permutation corresponding to the inversion sets interpreted as binary numbers (A211362) ordered by value.
27 2012-06-03 A211364 tabf,view Inversion sets of finite permutations that have only 0s and 1s in their inversion vectors.
28 2012-06-22 A211365 tabl,a Array read by antidiagonals: T(m,n) = Sum(1<=i<=m) i * (2m+n-1-i)!
29 2012-07-07 A211366 tabl,a Array read by antidiagonals: T(m,n) = Sum(1<=i<=m) i * ( n + 2(i-1) )!
30 2012-07-07 A211367 tabl,a Array read by antidiagonals: T(m,n) = m * Sum(1<=i<=m) (m+n-2+i)!
31 2012-07-07 A211368 tabl,a Array read by antidiagonals: T(m,n) = Sum(1<=i<=m) ( n + 2(i-1) )!
32 2012-07-07 A211369 smi tabl,a Array read by antidiagonals: T(m,n) = m*(m+n-1)! + Sum( n <= i <= m+n-2 ) i!
33 2012-07-07 A211370 smi tabl,a Array read by antidiagonals: T(m,n) = Sum( n <= i <= m+n-1 ) i!.
34 2012-07-24 A211344 smi tabl,t Atomic Boolean functions interpreted as binary numbers.
35 2013-03-21 A223537 tabl,a Compressed nim-multiplication table read by antidiagonals.
36 2013-03-21 A223538 tabl,a Key-matrix of compressed nim-multiplication table (A223537) read by antidiagonals.
37 2013-03-21 A223539 smi tabf,view List of entries in the compressed nim-multiplication table (A223537).
38 2013-03-21 A223540 tabl Matrix T(m,n) = nim-product(2^m,2^n) read by rows of lower triangle.
39 2013-03-21 A223541 sym,rows tabl,a Matrix T(m,n) = nim-product(2^m,2^n) read by antidiagonals.
40 2013-03-21 A223542 sym,rows tabl,a Key-matrix of A223541 (nim-products of powers of 2) read by antidiagonals.
41 2013-03-21 A223543 smi Nim-products of powers of 2, list of entries in matrix A223541.
42 2013-07-22 A227722 smi Smallest Boolean functions from small equivalence classes (counted by A000231).
43 2013-07-22 A227723 smi Smallest Boolean functions from big equivalence classes (counted by A000616).
44 2013-07-22 A227724 tabl,t T(n,k) = number of small equivalence classes of half full n-ary Boolean functions that contain 2^k functions.
45 2013-07-22 A227725 smi,rows tabl,t T(n,k) = number of small equivalence classes of n-ary Boolean functions that contain 2^k functions.
46 2013-08-01 A227960 smi tabf(diff(A006116)),view Big equivalence classes (A227723) related to subgroups of nimber addition (A190939).
47 2013-08-01 A227961 tabf(A000079) Triangle T(n,k) read by rows: how often does k appear among the first A006116(n) entries of A198260?
48 2013-08-04 A227962 perm,rows tabf(A076766) Triangle of permutations that assign sona-becs (A227960) to their complements.
49 2013-08-08 A227963 Small equivalence classes (A227722) of subgroups of nimber addition (A190939).
50 2013-08-24 A228539 tabf(A000079) Rows of binary Walsh matrices interpreted as reverse binary numbers.
51 2013-08-24 A228540 tabf(A000079) Rows of negated binary Walsh matrices interpreted as reverse binary numbers.
52 2013-08-25 A195467 perm,rows tablf Consecutive powers of the Gray code permutation.
53 2013-11-26 A232598 tabl,t T(n,k) = Stirling2(n,k) * OrderedBell(k)
54 2014-03-14 A239303 tabl,t Triangle of compressed square roots of Gray code * bit-reversal permutation.
55 2014-03-14 A239304 perm,rows tabl,t Triangle of permutations corresponding to the compressed square roots of Gray code * bit-reversal permutation (A239303).
56 2014-10-28 A248827 smi Row sums of A187783 and A089759.
57 2014-10-29 A248814 smi (6n)!/(6!^n).
58 2014-10-31 A249543 tabl,a Square array T(m,n) of integer partitions with m addends n+1, read by antidiagonals.
59 2014-10-31 A249544 tabl,a Array T(m,n) = binary palindrome with m runs of n ones, read by antidiagonals.
60 2014-11-02 A249615 tabf(diff(A000110)),view Number of non-singleton blocks in the n-th set partition (A231428).
61 2014-11-02 A249616 tabf(diff(A000110)),view Number of elements in non-singleton blocks in the n-th set partition (A231428).
62 2014-11-02 A249617 tabf(diff(A000110)),view Integer partition (A194602) of the n-th set partition (A231428).
63 2014-11-02 A249618 tabf(diff(A000142)),view Set partition (A231428) corresponding to the n-th finite permutation (A055089).
64 2014-11-04 A249619 tabf(A000041) Triangle T(m,n) = number of permutations of a multiset with m elements and signature corresponding to n-th integer partition (A194602).
65 2014-11-04 A249620 tabf(A000041) Triangle T(m,n) = number of partitions of multiset with m elements and signature corresponding to n-th integer partition (A194602).
66 2014-11-10 A248374 smi The integer partition a(n) (compare A194602) has only the non-one addends n+1 and 2.
67 2014-11-10 A250002 sym(rows) tabl,t Number of inequivalent binary linear [n,k] codes minus C(n,k).
68 2014-11-10 A250003 smi Number of inequivalent binary linear codes of length n minus 2^n.
69 2016-02-21 A269298 mi Central non-zero values of A231599.
70 2016-12-31 A280318 perm tabf(diff(A000142)),view a(n) is the n-th permutation generated by Heap's algorithm, represented by row number of A055089.
71 2016-12-31 A280319 perm,rows tabf(A000142) Irregular triangle read by rows: T(m, n) is the n-th permutation of m things generated by the Steinhaus-Johnson-Trotter algorithm, represented by row number of A055089.
72 2018-03 A300693 smi a(n) = number of edges in a concertina n-cube.
73 2018-03 A300694 smi a(n) = number of edges in a cocoon concertina n-cube.
74 2018-03 A300695 sym,rows tabf(A000124) Irregular triangle read by rows: T(n, k) = number of vertices with rank k in cocoon concertina n-cube.
75 2018-03 A300696 smi a(n) is the number of n-place formulas in first-order logic when variables are allowed to coincide.
76 2018-03 A300697 smi Volumes of concertina hypercubes.
77 2018-03 A300698 smi Half volumes of concertina hypercubes: a(n) = A300697(n)/2.
78 2018-03 A300699 sym,rows tabf(A000124) Irregular triangle read by rows: T(n, k) = number of vertices with rank k in concertina n-cube.
79 2018-03 A300700 tabl,t Triangle read by rows: T(n, n-k) = number of k-faces of the concertina n-cube.
80 2018-03 A300701 smi a(n) = number of hyperfaces in a concertina n-cube.