OFFSET
1,2
LINKS
Pontus von Brömssen, Rows n = 1..40, flattened
Jeffrey Shallit, What this country needs is an 18¢ piece, The Mathematical Intelligencer 25 (2003), issue 2, 20-23.
Jeffrey Shallit, What this country needs is an 18¢ piece.
Wikipedia, Change-making problem
FORMULA
EXAMPLE
Triangle begins:
n\k| 1 2 3 4 5 6 7 8 9 10 11 12
---|-------------------------------------
1 | 1
2 | 3 2
3 | 6 4 3
4 | 10 6 5 4
5 | 15 9 7 6 5
6 | 21 11 9 8 7 6
7 | 28 14 11 10 9 8 7
8 | 36 18 13 12 11 10 9 8
9 | 45 21 16 14 13 12 11 10 9
10 | 55 25 19 16 15 14 13 12 11 10
11 | 66 30 22 18 17 16 15 14 13 12 11
12 | 78 33 24 20 19 18 17 16 15 14 13 12
For n = 8, there is a unique optimal 3-coin system (1,3,4), with the representations
1 = 1
2 = 1 + 1
3 = 3
4 = 4
5 = 4 + 1
6 = 3 + 3
7 = 4 + 3
8 = 4 + 4
with a total of 13 = T(8,3) terms.
Shallit (2003) shows that T(99,k) is 4950, 900, 515, 389, 329, 292, 265 for k = 1..7.
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Pontus von Brömssen, Nov 30 2020
STATUS
approved