A390546 Triangle read by rows: T(n,k) = number of heapable permutations of length n that contain the max element on position k (positions starting from 0).

1, 0, 1, 0, 1, 1, 0, 1, 2, 2, 0, 2, 5, 5, 5, 0, 5, 15, 17, 17, 17, 0, 17, 58, 71, 71, 71, 71, 0, 71, 268, 351, 359, 359, 359, 359, 0, 359, 1471, 2035, 2126, 2126, 2126, 2126, 2126, 0, 2126, 9336, 13538, 14446, 14495, 14495, 14495, 14495, 14495

Offset

1,9

Comments

A permutation is heapable if its elements can be inserted into a binary min-heap in breadth-first order without violating the heap property.

Links

Sean A. Irvine, Table of n, a(n) for n = 1..120 (rows 1..15 flattened)

Benjamin Chen, Michael Cho, Mario Tutuncu-Macias, and Tony Tzolov, Efficient methods of calculating the number of heapable permutations, Discrete Applied Mathematics Volume 331, 31 May 2023, Pages 126-137.

Manolopoulos Panagiotis, Python Program

Example

Triangle begins:
  1
  0,  1
  0,  1,  1
  0,  1,  2,  2
  0,  2,  5,  5,  5
  0,  5, 15, 17, 17, 17
  0, 17, 58, 71, 71, 71, 71

Crossrefs

Cf. A336282 (number of heapable permutations), A390273 (total sums of heights), A390377 (the triangle for positions of 2), A390450 (sums of positions of 2).

Sequence in context: A008281 A094671 A354826 * A202015 A193350 A021458

Adjacent sequences: A390543 A390544 A390545 * A390547 A390548 A390549

Keyword

nonn,tabl

Author

Manolopoulos Panagiotis, Nov 10 2025

Extensions

More terms from Sean A. Irvine, Nov 23 2025

Status

approved