OFFSET
0,5
COMMENTS
The procedure to build the present triangle is as follows:
- row 0 contains a single 1:
. 1
- row 1 is added below, each new term is the sum of the adjacent prior terms:
. 1
. ---
. 1 1
- row 2 is added to the right, each new term is the sum of the adjacent prior terms:
. 1
. \
. 1 \ 2
. \
. 1 1 \ 1
- row 3 is added to the left, each new term is the sum of the adjacent prior terms:
. 1
. /
. 2 / 1
. /
. 2 / 1 2
. /
. 1 / 1 1 1
- row 4 is added below, each new term is the sum of the adjacent prior terms:
. 1
.
. 2 1
.
. 2 1 2
.
. 1 1 1 1
. ---------------
. 1 2 2 2 1
- and so on.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 0..10010
Rémy Sigrist, Illustration of the odd terms among the first 2^9 rows
Rémy Sigrist, PARI program
FORMULA
T(n, 0) = T(n, n) = 1.
T(n, k) = T(n, n-k).
EXAMPLE
Triangle begins:
1;
1, 1;
1, 2, 1;
1, 2, 2, 1;
1, 2, 2, 2, 1;
1, 2, 3, 3, 2, 1;
1, 2, 3, 4, 3, 2, 1;
1, 2, 3, 4, 4, 3, 2, 1;
1, 2, 3, 5, 6, 5, 3, 2, 1;
1, 2, 3, 5, 7, 7, 5, 3, 2, 1;
1, 2, 3, 5, 7, 8, 7, 5, 3, 2, 1;
1, 2, 3, 5, 8, 11, 11, 8, 5, 3, 2, 1;
1, 2, 3, 5, 8, 12, 14, 12, 8, 5, 3, 2, 1;
...
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Rémy Sigrist, Jul 17 2022
STATUS
approved