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

1,4

Comments

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

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.)

Formula

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

Example

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.

Crossrefs

Cf. A007318, A141481, A334688.

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

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

Sequence in context: A024699 A083479 A112231 * A213856 A173329 A369113

Adjacent sequences: A334739 A334740 A334741 * A334743 A334744 A334745

Keyword

nonn,nice

Author

Alec Jones and Peter Kagey, May 09 2020

Status

approved