A049286 Triangle of partitions v(d,c) defined in A002572.

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, 510

Offset: 1

Author

N. J. A. Sloane, Michael Somos

Keywords

• nonn
• tabl
• nice
• easy

Comments

Rows are the columns in the table at the end of the Minc reference, read top to bottom. - Joerg Arndt, Jan 15 2024

Examples

			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
		

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.

Crossrefs

Cf. A002572, A002573, A002574, A049284, A049285.

See A047913 for another version.

Programs

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 *)