OFFSET
1,2
COMMENTS
The triangle acts as a transform converting any sequence S(k) into a triangle with row sums = S(k). By way of example, begin with S(k), the primes: (2, 3, 5, 7, 11, ...). Add (0, 1, 2, 3, 4, ...) to the sequence getting (prime(n)+(n-1)) = (2, 4, 7, 10, 15, 18, 23, 36, 31, ...) = sequence Q(k). Then replace column 1 (1, 2, 3, ...) of triangle A143349 with sequence Q(k). This = triangle A143350 with row sums prime(n):
2;
4, -1;
7, -1, -1;
10, -2, -1, 0;
...
EXAMPLE
First few rows of the triangle:
1;
2, -1;
3, -1, -1;
4, -2, -1, 0;
5, -2, -1, 0, -1;
6, -3, -2, 0, -1, 1;
7, -3, -2, 0, -1, 1, -1;
8, -4, -2, 0, -1, 1, -1, 0;
9, -4, -3, 0, -1, 1, -1, 0, 0;
10, -5, -3, 0, -2, 1, -1, 0, 0, 1;
11, -5, -3, 0, -2, 1, -1, 0, 0, 1, -1;
12, -6, -4, 0, -2, 2, -1, 0, 0, 1, -1, 0;
13, -6, -4, 0, -2, 2, -1, 0, 0, 1, -1, 0, -1;
14, -7, -4, 0, -2, 2, -2, 0, 0, 1, -1, 0, -1, 1;
...
CROSSREFS
KEYWORD
tabl,sign
AUTHOR
Gary W. Adamson, Aug 10 2008
EXTENSIONS
a(39) ff. corrected by Georg Fischer, Jun 05 2023
STATUS
approved