This site is supported by donations to The OEIS Foundation.

# User:Tilman Piesk/list

## Contents

## 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. |