A334742 Pascal's spiral: starting with a(1) = 1, proceed in a square spiral, computing each term as the sum of horizontally and vertically adjacent prior terms.

1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 10, 12, 12, 14, 17, 20, 20, 23, 27, 32, 37, 37, 42, 48, 55, 62, 62, 69, 77, 87, 99, 111, 111, 123, 137, 154, 174, 194, 194, 214, 237, 264, 296, 333, 370, 370, 407, 449, 497, 552, 614, 676, 676, 738, 807, 884, 971, 1070

Offset: 1

Author

Alec Jones and Peter Kagey, May 09 2020

Keywords

• nonn
• nice

Comments

This is the square spiral analogy of Pascal's triangle thought of as a table read by antidiagonals.

Examples

			Spiral begins:
  111--99--87--77--69--62
                        |
   12--12--10---8---7  62
    |               |   |
   14   2---2---1   7  55
    |   |       |   |   |
   17   3   1---1   6  48
    |   |           |   |
   20   3---4---5---5  42
    |                   |
   20--23--27--32--37--37
a(15) = 10 = 8 + 2, the sum of the cells immediately to the right and below. The term to the left is not included in the sum because it has not yet occurred in the spiral.
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..10000
• Peter Kagey, Bitmap illustrating the parity of the first 2^20=1048576 terms. (Even and odd numbers are represented with black and white pixels respectively.)

Crossrefs

Cf. A007318, A141481, A334688.

Cf. A180714, A214526, A274640, A278180, A304586, A307834, A334741.

x- and y-coordinates are given by A174344 and A274923, respectively.

Formula

a(A033638(n)) = a(A002620(n)) for n > 1.