A361070 - OEIS

%I #8 Mar 02 2023 11:24:41

%S 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,

%T 107,115,126,132,145,153,163,175,182,199,206,220,232,242,259,268,285,

%U 297,310,328,337,359,370,387,404,416,440,451,472,489,504,528,540

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

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

%C   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

%C   . . . . . . . . . . . . . . . . . . . . . . . . . 5 6 6 6 6 6

%C   . . . . . . . . . . . . . . . . . . . . 6 4 5 5 5 5 6 6 6 6 6

%C   . . . . . . . . . . . . . . . . 6 5 3 4 4 4 5 5 5 5 6 6 6 6 .

%C   . . . . . . . . . . . . 6 6 5 4 2 3 3 4 4 4 5 5 5 6 6 6 6 . .

%C   . . . . . . . . . 6 6 5 5 4 3 1 2 3 3 4 4 5 5 5 6 6 6 . . . .

%C   . . . . . . 6 6 6 5 5 4 4 3 2 0 2 3 4 4 5 5 6 6 6 . . . . . .

%C   . . . . 6 6 6 5 5 5 4 4 3 3 2 1 3 4 5 5 6 6 . . . . . . . . .

%C   . . 6 6 6 6 5 5 5 4 4 4 3 3 2 4 5 6 6 . . . . . . . . . . . .

%C   . 6 6 6 6 5 5 5 5 4 4 4 3 5 6 . . . . . . . . . . . . . . . .

%C   6 6 6 6 6 5 5 5 5 4 6 . . . . . . . . . . . . . . . . . . . .

%C   6 6 6 6 6 5 . . . . . . . . . . . . . . . . . . . . . . . . .

%C   6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

%H Rémy Sigrist, <a href="/A361070/a361070.txt">C++ program</a>

%e Square array A360923 begins as follows:

%e      0 2 3 4 4 5 5 6 6 6 7 7 7 8 8 8 8 .

%e      1 3 4 5 5 6 6 7 7 7 8 8 8 . . . . .

%e      4 5 6 6 7 7 8 8 8 . . . . .

%e      7 7 8 8 . . . . . .

%e      . . . . .

%e 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.

%o (C++) See Links section.

%Y Cf. A002620, A051890, A360923.

%K nonn

%O 0,4

%A _Rémy Sigrist_, Mar 01 2023