A361070 a(n) is the number of occurrences of n in A360923.

1, 1, 1, 2, 4, 5, 7, 10, 12, 15, 19, 21, 27, 30, 35, 40, 44, 52, 56, 63, 70, 75, 85, 90, 100, 107, 115, 126, 132, 145, 153, 163, 175, 182, 199, 206, 220, 232, 242, 259, 268, 285, 297, 310, 328, 337, 359, 370, 387, 404, 416, 440, 451, 472, 489, 504, 528, 540

Offset: 0

Author

Rémy Sigrist, Mar 01 2023

Keywords

• nonn

Comments

For n > 0, the number of starting positions from Z^2 at distance n from (0, 0) appears to be A051890(n):

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

. . . . . . . . . . . . . . . . . . . . . . . . . 5 6 6 6 6 6

. . . . . . . . . . . . . . . . . . . . 6 4 5 5 5 5 6 6 6 6 6

. . . . . . . . . . . . . . . . 6 5 3 4 4 4 5 5 5 5 6 6 6 6 .

. . . . . . . . . . . . 6 6 5 4 2 3 3 4 4 4 5 5 5 6 6 6 6 . .

. . . . . . . . . 6 6 5 5 4 3 1 2 3 3 4 4 5 5 5 6 6 6 . . . .

. . . . . . 6 6 6 5 5 4 4 3 2 0 2 3 4 4 5 5 6 6 6 . . . . . .

. . . . 6 6 6 5 5 5 4 4 3 3 2 1 3 4 5 5 6 6 . . . . . . . . .

. . 6 6 6 6 5 5 5 4 4 4 3 3 2 4 5 6 6 . . . . . . . . . . . .

. 6 6 6 6 5 5 5 5 4 4 4 3 5 6 . . . . . . . . . . . . . . . .

6 6 6 6 6 5 5 5 5 4 6 . . . . . . . . . . . . . . . . . . . .

6 6 6 6 6 5 . . . . . . . . . . . . . . . . . . . . . . . . .

6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The largest column of A360923 containing n appears to have index A002620(n).

Examples

			Square array A360923 begins as follows:
     0 2 3 4 4 5 5 6 6 6 7 7 7 8 8 8 8 .
     1 3 4 5 5 6 6 7 7 7 8 8 8 . . . . .
     4 5 6 6 7 7 8 8 8 . . . . .
     7 7 8 8 . . . . . .
     . . . . .
Hence a(0) = 1, a(1) = 1, a(2) = 1, a(3) = 2, a(4) = 4, a(5) = 5, a(6) = 7, a(7) = 10 and a(8) = 12.
		

Links

• Rémy Sigrist, C++ program

Crossrefs

Cf. A002620, A051890, A360923.