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

5,1

Comments

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

Links

Table of n, a(n) for n=5..34.

Formula

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

Example

                          _____    __         ______________
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.

Sequence in context: A124510 A131886 A265014 * A262243 A328964 A061284

Adjacent sequences: A378941 A378942 A378943 * A378945 A378946 A378947

Keyword

nonn,tabf,more

Author

Roger Ford, Dec 11 2024

Status

approved