A374921 Irregular triangle read by rows: T(n,k), n >= 0, k >= 1, in which if n is even then row n lists the first A008619(n) even indexed terms of A027336 otherwise if n is odd then row n lists the first A008619(n) odd indexed terms of A027336.

1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 2, 4, 1, 1, 3, 6, 1, 2, 4, 8, 1, 1, 3, 6, 11, 1, 2, 4, 8, 15, 1, 1, 3, 6, 11, 20, 1, 2, 4, 8, 15, 26, 1, 1, 3, 6, 11, 20, 35, 1, 2, 4, 8, 15, 26, 45, 1, 1, 3, 6, 11, 20, 35, 58, 1, 2, 4, 8, 15, 26, 45, 75, 1, 1, 3, 6, 11, 20, 35, 58, 96, 1, 2, 4, 8, 15, 26, 45, 75, 121

Offset

0,6

Comments

The sum of row n equals the number of partitions of n.

Links

Table of n, a(n) for n=0..89.

Example

Triangle begins:
  1;
  1;
  1, 1;
  1, 2;
  1, 1, 3;
  1, 2, 4;
  1, 1, 3, 6;
  1, 2, 4, 8;
  1, 1, 3, 6, 11;
  1, 2, 4, 8, 15;
  1, 1, 3, 6, 11, 20;
  1, 2, 4, 8, 15, 26;
  1, 1, 3, 6, 11, 20, 35;
  1, 2, 4, 8, 15, 26, 45;
  1, 1, 3, 6, 11, 20, 35, 58;
  1, 2, 4, 8, 15, 26, 45, 75;
  1, 1, 3, 6, 11, 20, 35, 58, 96;
  1, 2, 4, 8, 15, 26, 45, 75, 121;
  ...
For n = 10 the sum of the 10th row is 1 + 1 + 3 + 6 + 11 + 20 = 42, the same as the number of partitions of 10.

Crossrefs

Row sums give A000041.

Row lengths give A008619.

Right border gives A027336.

Columns 1..4: A000012, A000034, A010702, A010724.

Cf. A058695, A058696, A002865, A167430, A176206, A182844, A182845, A336811, A338156.

Sequence in context: A358169 A327392 A112798 * A187846 A181087 A029288

Adjacent sequences: A374918 A374919 A374920 * A374922 A374923 A374924

Keyword

nonn,tabf

Author

Omar E. Pol, Aug 01 2024

Status

approved