A359251 Sum of terms in an odd-even expansion of n.

2, 3, 10, 11, 14, 15, 32, 33, 36, 37, 60, 61, 64, 65, 110, 111, 114, 115, 124, 125, 128, 129, 176, 177, 180, 181, 234, 235, 238, 239, 342, 343, 346, 347, 356, 357, 360, 361, 380, 381, 384, 385, 470, 471, 474, 475, 578, 579, 582, 583, 592, 593, 596, 597, 622, 623, 626, 627, 792, 793, 796, 797

Offset

2,1

Comments

n stands alone in the first row, and then each row expands to a new row as follows.

An even number 2b >= 2 or an odd number 2c+1 >= 3 expands into cells below, below left, and below right, as follows:

even odd

2b 2c+1

b 0 b c 1 c

When expansions overlap, the values add together in the new cells.

Any 0 or 1 does not expand and expansions end when a row of only 0's and 1's is reached.

This last row is 1,1,1 when n=3 and otherwise always 1,0,1.

a(n) is the sum of all cells in all rows, excluding the starting n itself.

Links

Table of n, a(n) for n=2..63.

Example

For n = 4:
      4       initial row
    2 0 2
  1 0 2 0 1
    1 0 1     last row
  a(4) = (2+2) + (1+2+1) + (1+1).
For n = 8:
        8
      4 0 4
    2 0 4 0 2
  1 0 3 0 3 0 1
    1 1 2 1 1
      1 0 1
  a(8) = (4+4) + (2+4+2) + (1+3+3+1) + (1+1+2+1+1) + (1+1) = 32.

Crossrefs

Sequence in context: A250174 A285622 A081706 * A032804 A248407 A047473

Adjacent sequences: A359248 A359249 A359250 * A359252 A359253 A359254

Keyword

nonn,easy

Author

Moosa Nasir, Dec 22 2022

Status

approved