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

1,4

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

Table of n, a(n) for n=1..79.

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

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

See A047913 for another version.

Sequence in context: A175331 A098805 A168396 * A308477 A079216 A181654

Adjacent sequences: A049283 A049284 A049285 * A049287 A049288 A049289

Keyword

nonn,tabl,nice,easy

Author

N. J. A. Sloane, Michael Somos

Status

approved