OFFSET
3,5
COMMENTS
T(n,m) is a triangle, read by rows.
LINKS
Rainer Rosenthal, Rows n = 3..100, flattened
Hugo Pfoertner, PARI program
EXAMPLE
The triangle begins
\ m 3 4 5 6 7 8 9 10
n \-------------------------------------
3 | 0, | | | | | | |
4 | 0, 0, | | | | | |
5 | 0, 3, 1, | | | | |
6 | 1, 7, 12, 11, | | | |
7 | 1, 11, 26, 52, 40, | | |
8 | 4, 23, 50, 94, 147, 105, | |
9 | 4, 30, 69, 127, 198, 301, 190, |
10 | 10, 49, 103, 192, 302, 444, 583, 379
.
.
4 | . C . . . There are six squared distances.
3 | . . . . . They are arranged as follows:
2 | D . . . B AB-BC-CD-DA (counterclockwise)
1 | . A . . . AC X DB (across)
y /---------- Here: AB = 3^2 + 1^2 = 10,
x 1 2 3 4 5 BC = 13, CD = 5, DA = 2,
. AC = 9, DB = 16
10-13-5-2 <==== yielding this
9 X 16 <==== description
.
.
T(5,4) = a(5) = 3:
.
4 | . X . . . 4 | . X . . . 4 | . . X . .
3 | . . . . . 3 | . . . . X 3 | . . . . X
2 | X . . . X 2 | X . . . . 2 | X . . . .
1 | . X . . . 1 | . X . . . 1 | . X . . .
y /---------- y /---------- y /----------
x 1 2 3 4 5 x 1 2 3 4 5 x 1 2 3 4 5
.
10-13-5-2 13-10-5-2 13-5-8-2
9 X 16 9 X 17 10 X 17
.
T(5,5) = a(6) = A353447(5) = 1:
.
5 | . . . X .
4 | . . . . .
3 | . . . . X 13-5-18-2
2 | X . . . . 20 X 17
1 | . X . . .
y /----------
x 1 2 3 4 5
.
T(6,3) = a(7) = 1:
.
3 | . . . X . .
2 | X . . . . X 17-5-10-2
1 | . X . . . . 8 X 25
y /------------
x 1 2 3 4 5 6
.
T(6,4) = a(8) = 7:
.
4 | . X . . . . 4 | . X . . . . 4 | . . X . . . 4 | . . . X . .
3 | . . . . . . 3 | . . . . . X 3 | . . . . . . 3 | X . . . . .
2 | X . . . . X 2 | X . . . . . 2 | X . . . . X 2 | . . . . . X
1 | . X . . . . 1 | . X . . . . 1 | . X . . . . 1 | . X . . . .
y /------------ y /------------ y /------------ y /------------
x 1 2 3 4 5 6 x 1 2 3 4 5 6 x 1 2 3 4 5 6 x 1 2 3 4 5 6
.
17-20-5-2 20-17-5-2 17-13-8-2 17-8-10-5
9 X 25 9 X 26 10 X 25 13 X 26
.
4 | . . . . X . 4 | . . X . . . 4 | . . X . . .
3 | . . . . . . 3 | . . . . . . 3 | . . . . . X
2 | X . . . . X 2 | X . . . . X 2 | X . . . . .
1 | . X . . . . 1 | . . X . . . 1 | . . X . . .
y /------------ y /------------ y /------------
x 1 2 3 4 5 6 x 1 2 3 4 5 6 x 1 2 3 4 5 6
.
17-5-20-2 10-13-8-5 13-10-8-5
18 X 25 9 X 25 9 X 26
.
PROG
(PARI) see Pfoertner link.
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Hugo Pfoertner and Rainer Rosenthal, May 02 2022
STATUS
approved