OFFSET
1,2
COMMENTS
Officially the borders are read starting at the bottom left, reading horizontally until the main diagonal is reached, and then reading vertically upwards until the top row is reached.
However, in this case both borders are symmetric about their midpoints, and the bottom border is the same as the right-hand border, so the direction in which the borders are read is less critical.
LINKS
R. J. Mathar, Table of n, a(n) for n = 1..10000
EXAMPLE
The array in A072030 begins:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...
2, 1, 3, 2, 4, 3, 5, 4, 6, 5, ...
3, 3, 1, 4, 4, 2, 5, 5, 3, 6, ...
4, 2, 4, 1, 5, 3, 5, 2, 6, 4, ...
5, 4, 4, 5, 1, 6, 5, 5, 6, 2, ...
6, 3, 2, 3, 6, 1, 7, 4, 3, 4, ...
7, 5, 5, 5, 5, 7, 1, 8, 6, 6, ...
8, 4, 5, 2, 5, 4, 8, 1, 9, 5, ...
9, 6, 3, 6, 6, 3, 6, 9, 1, 10, ...
10, 5, 6, 4, 2, 4, 6, 5, 10, 1, ...
...
The successive bottom and right-hand borders are:
1,
2, 1, 2,
3, 3, 1, 3, 3,
4, 2, 4, 1, 4, 2, 4,
5, 4, 4, 5, 1, 5, 4, 4, 5,
6, 3, 2, 3, 6, 1, 6, 3, 2, 3, 6,
7, 5, 5, 5, 5, 7, 1, 7, 5, 5, 5, 5, 7,
...
MAPLE
A267177 := proc(n, k)
if k <= n then
A072030(n, k) ;
else
A072030(2*n-k, n) ;
end if;
end proc:
seq(seq(A267177(n, k), k=1..2*n-1), n=1..10) ; # R. J. Mathar, May 07 2016
MATHEMATICA
A072030[n_, k_] := A072030[n, k] = Which[n < 1 || k < 1, 0, n == k, 1, n < k, A072030[k, n], True, 1+A072030[k, n-k]];
Table[A267177[n, k], {n, 1, 10}, {k, 1, 2n-1}] // Flatten (* Jean-François Alcover, Apr 23 2023, after R. J. Mathar *)
PROG
(PARI) \\ Based on Michel Marcus's program for A049834.
tabl(nn) = {for (n=1, nn,
for (k=1, n, a = n; b = k; r = 1; s = 0; while (r, q = a\b; r = a - b*q; s += q; a = b; b = r); print1(s, ", "); );
for (k=1, n-1, a = n; b = n-k; r = 1; s = 0; while (r, q = a\b; r = a - b*q; s += q; a = b; b = r); print1(s, ", "); );
print(); ); }
tabl(12)
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
N. J. A. Sloane, Jan 14 2016
STATUS
approved