login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A332353 Triangle read by rows: T(m,n) = Sum_{-m<i<m, -n<j<n, gcd{i,j}=2} (m-|i|)*(n-|j|)/2, m >= n >= 1. 2
0, 0, 0, 1, 2, 8, 2, 4, 14, 24, 3, 6, 22, 38, 60, 4, 8, 30, 52, 82, 112, 5, 10, 40, 70, 112, 154, 212, 6, 12, 50, 88, 142, 196, 270, 344, 7, 14, 62, 110, 178, 246, 340, 434, 548, 8, 16, 74, 132, 214, 296, 410, 524, 662, 800, 9, 18, 88, 158, 258, 358, 498, 638, 808, 978, 1196 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
This is the triangle in A332352, halved.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..11325 (rows 1..150 of the triangle, flattened)
M. A. Alekseyev, M. Basova, and N. Yu. Zolotykh. On the minimal teaching sets of two-dimensional threshold functions. SIAM Journal on Discrete Mathematics 29:1 (2015), 157-165. doi:10.1137/140978090. This sequence is f_2(m,n)/2.
EXAMPLE
Triangle begins:
0,
0, 0,
1, 2, 8,
2, 4, 14, 24,
3, 6, 22, 38, 60,
4, 8, 30, 52, 82, 112,
5, 10, 40, 70, 112, 154, 212,
6, 12, 50, 88, 142, 196, 270, 344,
7, 14, 62, 110, 178, 246, 340, 434, 548,
8, 16, 74, 132, 214, 296, 410, 524, 662, 800,
...
MAPLE
VR := proc(m, n, q) local a, i, j; a:=0;
for i from -m+1 to m-1 do for j from -n+1 to n-1 do
if gcd(i, j)=q then a:=a+(m-abs(i))*(n-abs(j)); fi; od: od: a; end;
for m from 1 to 12 do lprint(seq(VR(m, n, 2)/2, n=1..m), ); od:
MATHEMATICA
A332353[m_, n_]:=Sum[If[GCD[i, j]==2, 2(m-i)(n-j), 0], {i, 2, m-1, 2}, {j, 2, n-1, 2}]+If[n>2, m*n-2m, 0]+If[m>2, m*n-2n, 0]; Table[A332353[m, n], {m, 15}, {n, m}] (* Paolo Xausa, Oct 18 2023 *)
CROSSREFS
The main diagonal is A177719.
Sequence in context: A074962 A064863 A021358 * A203022 A224196 A141449
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Feb 10 2020
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 4 22:58 EDT 2024. Contains 372257 sequences. (Running on oeis4.)