OFFSET
1,4
COMMENTS
Rows are the columns in the table at the end of the Minc reference, read top to bottom. - Joerg Arndt, Jan 15 2024
LINKS
Shimon Even and Abraham Lempel, Generation and enumeration of all solutions of the characteristic sum condition, Information and Control 21 (1972), 476-482.
H. Minc, A problem in partitions: Enumeration of elements of a given degree in the free commutative entropic cyclic groupoid, Proc. Edinburgh Math. Soc. (2) 11 1958/1959 223-224.
EXAMPLE
Triangle begins
1,
1, 1,
2, 1, 1,
3, 2, 1, 1,
5, 4, 2, 1, 1,
9, 7, 4, 2, 1, 1,
16, 12, 7, 4, 2, 1, 1,
28, 22, 13, 7, 4, 2, 1, 1,
50, 39, 24, 13, 7, 4, 2, 1, 1,
89, 70, 42, 24, 13, 7, 4, 2, 1, 1,
159, 126, 76, 43, 24, 13, 7, 4, 2, 1, 1,
285, 225, 137, 78, 43, 24, 13, 7, 4, 2, 1, 1,
...
Rows read backward approach A002843. - Joerg Arndt, Jan 15 2024
MAPLE
v := proc(c, d) option remember; local i; if d < 0 or c < 0 then 0 elif d = c then 1 else add(v(i, d-c), i=1..2*c); fi; end;
MATHEMATICA
v[c_, d_] := v[c, d] = If[d < 0 || c < 0, 0, If[d == c, 1, Sum[v[i, d - c], {i, 1, 2*c}]]]; Table[v[d, c], {c, 1, 13}, {d, 1, c}] // Flatten (* Jean-François Alcover, Dec 10 2012, after Maple *)
CROSSREFS
KEYWORD
AUTHOR
STATUS
approved