A365434 Irregular triangle read by rows: T(n,k) is the number of cubes in the k-th level of the ziggurat of order n described in A347186, n >= 1, k >= 1.

1, 3, 1, 4, 2, 7, 5, 3, 1, 6, 4, 2, 12, 9, 7, 5, 3, 1, 8, 6, 4, 2, 15, 13, 11, 9, 7, 5, 3, 1, 13, 9, 7, 5, 2, 18, 16, 14, 12, 10, 8, 6, 4, 2, 12, 10, 8, 6, 4, 2, 28, 24, 22, 20, 16, 14, 12, 9, 7, 5, 3, 1, 14, 12, 10, 8, 6, 4, 2, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 24, 19, 17, 15, 11, 9, 7, 3, 1, 1

Offset: 1

Author

Omar E. Pol, Oct 19 2023

Keywords

• nonn
• tabf

Comments

The values of n when the number of terms in row n is equal to n give A174973.

The values of n when the number of terms in row n is not equal to n give A238524.

If and only if n is a power of 2 then row n lists the first n odd numbers in decreasing order.

If and only if n is an odd prime then row n lists the first (n + 1)/2 positive even numbers in decreasing order.

If and only if n is an even perfect number then row n lists 2*n together with the first n - 1 odd numbers in decreasing order.

Examples

			Triangle begins:
   1;
   3,  1;
   4,  2;
   7,  5,  3,  1;
   6,  4,  2;
  12,  9,  7,  5,  3,  1;
   8,  6,  4,  2;
  15, 13, 11,  9,  7,  5,  3,  1;
  13,  9,  7,  5,  2;
  18, 16, 14, 12, 10,  8,  6,  4,  2;
  12, 10,  8,  6,  4,  2;
  28, 24, 22, 20, 16, 14, 12,  9,  7,  5,  3, 1;
  14, 12, 10,  8,  6,  4,  2;
  24, 22, 20, 18, 16, 14, 12, 10,  8,  6,  4, 2;
  24, 19, 17, 15, 11,  9,  7,  3,  1,  1;
  31, 29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1;
  ...
		

Crossrefs

Column 1 gives A000203.

Row sums give A347186.

Row lengths give A365433.

Cf. A000079, A000396, A065091, A174973, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A238524, A245092, A262626, A347263, A347367, A365195.