cp's OEIS Frontend

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.

%I A378944 #28 Dec 26 2024 13:27:09
%S A378944 2,4,8,6,20,12,48,24,28,132,60,56,348,144,112,162,1008,396,280,324,
%T A378944 2812,1044,672,648,1076,8420,3024,1848,1620,2152
%N 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.
%C A378944 The conjectured formula for the numbers in T(n,k) involves two unsolved sequences, semi-meanders and meandric numbers.
%F A378944 T(n,k) = 2 * A000682(n+1-2*k) * A077054(k-1).
%e A378944                           _____    __         ______________
%e A378944 Vertical lines = stamp#  |     |  |  |       |   __    __   |   __
%e A378944 Horizontal lines = folds 1  5  2  3  4       |  |  |  |  |  |  |  |
%e A378944                             |  |__|  |       1  6  5  4  3  2  8  7
%e A378944                             |________|          |  |__|  |__|     |
%e A378944      fold 4-5 covers stamp #2  k = 4/2          |_________________|
%e A378944                         Example: T(5,2)      fold 6-7 covers stamp #2 k = 6/2
%e A378944                                                                Example: T(8,3)
%e A378944 Irregular triangle begins:
%e A378944    n\k  (2)  (3)  (4)  (5)  (6)
%e A378944     5:   2
%e A378944     6:   4
%e A378944     7:   8    6
%e A378944     8:   20   12
%e A378944     9:   48   24   28
%e A378944    10:   132  60   56
%e A378944    11:   348  144  112  162
%e A378944    12:   1008 396  280  324
%e A378944    13:   2812 1044 672  648  1076
%e A378944    14:   8420 3024 1848 1620 2152
%Y A378944 Cf. A000682, A005316, A077054, A301620.
%K A378944 nonn,tabf,more
%O A378944 5,1
%A A378944 _Roger Ford_, Dec 11 2024