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

1,2

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.

Links

Table of n, a(n) for n=1..91.

Example

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.

Sequence in context: A351887 A273261 A274531 * A115659 A067060 A068028

Adjacent sequences: A365431 A365432 A365433 * A365435 A365436 A365437

Keyword

nonn,tabf

Author

Omar E. Pol, Oct 19 2023

Status

approved