A334745 Starting with a(1) = a(2) = 1, proceed in a square spiral, computing each term as the sum of diagonally adjacent prior terms.

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 3, 2, 3, 1, 1, 3, 2, 3, 1, 1, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 1, 1, 4, 3, 6, 3, 4, 1, 1, 4, 3, 6, 3, 4, 1, 1, 4, 4, 6, 6, 4, 4, 1, 1, 4, 4, 6, 6, 4, 4, 1, 1, 5, 4, 10, 6, 10, 4, 5, 1, 1, 5, 4, 10, 6

Offset

1,8

Links

Peter Kagey, Table of n, a(n) for n = 1..10000

Peter Kagey, Bitmap illustrating the parity of the first 2^22 terms. (Even and odd numbers are represented with black and white pixels respectively.)

Formula

Conjecture: a(2n-1) = A247976(n).

Example

Spiral begins:
... 3---3---3---3---1
                    |
1---1---2---2---1   1
|               |   |
2   1---1---1   1   3
|   |       |   |   |
2   1   1---1   2   2
|   |           |   |
1   1---2---1---1   3
|                   |
1---3---2---3---1---1
The last illustrated term above is a(35) = 3 = 2 + 1 because diagonally down-right is 2 and diagonally down-left is 1.

Crossrefs

Cf. A141481, A278180, A334741, A334742.

The x- and y-coordinates at n-th step are A174344 and A274923 respectively.

Sequence in context: A307017 A220424 A182907 * A323231 A175128 A359307

Adjacent sequences: A334742 A334743 A334744 * A334746 A334747 A334748

Keyword

nonn

Author

Alec Jones and Peter Kagey, May 09 2020

Status

approved