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A358574
Triangle read by rows: T(n,k) is the number of vertices formed when n points are placed along each edge of a square that divide the edges into n+1 equal parts and a line is continuously drawn from the current point to that k points, 2 <= k <= 2*n, counterclockwise around the square until the starting point is again reached.
3
8, 12, 20, 12, 16, 16, 16, 64, 16, 20, 36, 20, 68, 36, 100, 20, 24, 36, 24, 24, 44, 144, 29, 144, 24, 28, 28, 28, 92, 28, 140, 28, 44, 76, 208, 28, 32, 44, 32, 84, 52, 32, 39, 240, 88, 292, 46, 296, 32, 36, 48, 36, 80, 52, 164, 36, 252, 100, 316, 52, 368, 124, 364, 36, 40, 40, 40, 80, 40, 164, 47, 40, 112, 364, 40, 436, 144, 88, 67, 472, 40
OFFSET
1,1
COMMENTS
See A358556 for further details.
LINKS
Scott R. Shannon, Table for n=1..50.
Scott R. Shannon, Image for T(2,3) = 20.
Scott R. Shannon, Image for T(4,6) = 36.
Scott R. Shannon, Image for T(7,9) = 240.
Scott R. Shannon, Image for T(10,19) = 584.
Scott R. Shannon, Image for T(11,20) = 90.
Scott R. Shannon, Image for T(20,11) = 308.
Scott R. Shannon, Image for T(20,30) = 100.
Scott R. Shannon, Image for T(20,31) = 2220.
FORMULA
T(n,k) = A358627(n,k) - A358556(n,k) + 1 by Euler's formula.
T(n,2*n) = 4*(n + 1). The line cuts the square into two parts so no new vertices are created.
T(n,k) = 4*(n + 1) where k <= n and k|(4*n). Four lines cut across the square's corners so no new vertices are created.
EXAMPLE
The table begins:
8;
12, 20, 12;
16, 16, 16, 64, 16;
20, 36, 20, 68, 36, 100, 20;
24, 36, 24, 24, 44, 144, 29, 144, 24;
28, 28, 28, 92, 28, 140, 28, 44, 76, 208, 28;
32, 44, 32, 84, 52, 32, 39, 240, 88, 292, 46, 296, 32;
36, 48, 36, 80, 52, 164, 36, 252, 100, 316, 52, 368, 124, 364, 36;
40, 40, 40, 80, 40, 164, 47, 40, 112, 364, 40, 436, 144, 88, 67, 472, 40;
.
.
See the attached file for more examples.
CROSSREFS
Sequence in context: A168670 A291758 A232867 * A084488 A337877 A211410
KEYWORD
nonn,tabf
AUTHOR
Scott R. Shannon, Nov 23 2022
STATUS
approved