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.
81	2022-10	A358126	smi		Replace 2^k in binary expansion of n with 2^(2^k).
82	2022-11	A358167		tabf(A001146) for n > 0	T(n, k) = k-th fixed point in Zhegalkin permutation n (row n of A197819).