A378944 Triangle read by rows: T(n,k) = number of stamp foldings with stamp #1 first, n stamps and stamp #2 covered by exactly one fold. k = the stamp number before the fold covering stamp #2 divided by 2. See examples.

2, 4, 8, 6, 20, 12, 48, 24, 28, 132, 60, 56, 348, 144, 112, 162, 1008, 396, 280, 324, 2812, 1044, 672, 648, 1076, 8420, 3024, 1848, 1620, 2152

Offset: 5

Author

Roger Ford, Dec 11 2024

Keywords

• nonn
• tabf
• more

Comments

The conjectured formula for the numbers in T(n,k) involves two unsolved sequences, semi-meanders and meandric numbers.

Examples

			                          _____    __         ______________
Vertical lines = stamp#  |     |  |  |       |   __    __   |   __
Horizontal lines = folds 1  5  2  3  4       |  |  |  |  |  |  |  |
                            |  |__|  |       1  6  5  4  3  2  8  7
                            |________|          |  |__|  |__|     |
     fold 4-5 covers stamp #2  k = 4/2          |_________________|
                        Example: T(5,2)      fold 6-7 covers stamp #2 k = 6/2
                                                               Example: T(8,3)
Irregular triangle begins:
   n\k  (2)  (3)  (4)  (5)  (6)
    5:   2
    6:   4
    7:   8    6
    8:   20   12
    9:   48   24   28
   10:   132  60   56
   11:   348  144  112  162
   12:   1008 396  280  324
   13:   2812 1044 672  648  1076
   14:   8420 3024 1848 1620 2152
		

Crossrefs

Cf. A000682, A005316, A077054, A301620.

Formula

T(n,k) = 2 * A000682(n+1-2*k) * A077054(k-1).