A092113 Triangle read by rows: T(n,k) is the number of stacks of n pancakes requiring k = 0, ..., A058986(n) flips to sort.

1, 1, 1, 1, 2, 2, 1, 1, 3, 6, 11, 3, 1, 4, 12, 35, 48, 20, 1, 5, 20, 79, 199, 281, 133, 2, 1, 6, 30, 149, 543, 1357, 1903, 1016, 35, 1, 7, 42, 251, 1191, 4281, 10561, 15011, 8520, 455, 1, 8, 56, 391, 2278, 10666, 38015, 93585, 132697, 79379, 5804, 1, 9, 72, 575

Offset

1,5

Comments

Last term of row k is A067607(k).

Row n has length A058986(n) + 1. - Martin Renner, Jul 23 2017

Links

Sean A. Irvine, Table of n, a(n) for n = 1..97 (terms 1..68 from Martin Renner)

Example

Triangle begins:
  1;
  1,  1;
  1,  2,  2,  1;
  1,  3,  6, 11,  3;
  1,  4, 12, 35, 48, 20;
  ...
From Jon E. Schoenfield, Dec 16 2021: (Start)
For n=3, the 3! = 6 permutations are {1,2,3}, {1,3,2}, {2,1,3}, {2,3,1}, {3,1,2}, and {3,2,1}. Of these,
T(3,0)=1 permutation (namely, {1,2,3}) requires no prefix reversals (because it is already sorted);
T(3,1)=2 permutations (namely, {2,1,3} and {3,2,1}) require one prefix reversal, e.g., {2,1,3} -> {1,2,3};
T(3,2)=2 permutations (namely, {2,3,1} and {3,1,2}) require two prefix reversals, e.g., {2,3,1} -> {3,2,1} -> {1,2,3}; and
T(3,3)=1 permutation (namely, {1,3,2}) requires 3 prefix reversals: {1,3,2} -> {3,1,2} -> {2,1,3} -> {1,2,3};
thus, the terms in row n=3 are 1, 2, 2, 1. (End)

Crossrefs

Cf. A058986, A067607.

Sequence in context: A122888 A371830 A266378 * A331485 A342061 A045995

Adjacent sequences: A092110 A092111 A092112 * A092114 A092115 A092116

Keyword

nonn,tabf

Author

Eric W. Weisstein, Feb 21 2004

Status

approved