A331762 Triangle read by rows: T(n,k) (1 <= k <= n) = Sum_{i=1..n, j=1..k, gcd(i,j)=2} (n+1-i)*(k+1-j).

0, 0, 1, 0, 2, 4, 0, 4, 8, 15, 0, 6, 12, 22, 32, 0, 9, 18, 33, 48, 71, 0, 12, 24, 44, 64, 94, 124, 0, 16, 32, 58, 84, 123, 162, 211, 0, 20, 40, 72, 104, 152, 200, 260, 320, 0, 25, 50, 90, 130, 190, 250, 325, 400, 499

Offset

1,5

Links

Table of n, a(n) for n=1..55.

M. A. Alekseyev. On the number of two-dimensional threshold functions. SIAM J. Disc. Math. 24(4), 2010, pp. 1617-1631. doi:10.1137/090750184

M. A. Alekseyev, M. Basova, N. Yu. Zolotykh. On the minimal teaching sets of two-dimensional threshold functions. SIAM J. Disc. Math. 29(1), 2015, pp. 157-165.

Example

Triangle begins:
  0;
  0,  1;
  0,  2,  4;
  0,  4,  8,  15;
  0,  6, 12,  22,  32;
  0,  9, 18,  33,  48,  71;
  0, 12, 24,  44,  64,  94, 124;
  0, 16, 32,  58,  84, 123, 162, 211;
  0, 20, 40,  72, 104, 152, 200, 260, 320;
  0, 25, 50,  90, 130, 190, 250, 325, 400, 499;
  0, 30, 60, 108, 156, 228, 300, 390, 480, 598, 716;
  ...

Maple

V := proc(m, n, q) local a, i, j; a:=0;
for i from 1 to m do for j from 1 to n do
if gcd(i, j)=q then a:=a+(m+1-i)*(n+1-j); fi; od: od: a; end;
for m from 1 to 12 do
lprint([seq(V(m, n, 2), n=1..m)]); od:

Mathematica

Table[Sum[Boole[GCD[i, j] == 2] (n + 1 - i) (k + 1 - j), {i, n}, {j, k}], {n, 11}, {k, n}] // Flatten (* Michael De Vlieger, Feb 04 2020 *)

Crossrefs

Cf. A115004, A114999, A320541.

The main diagonal is A331761.

See A335683 for another version.

Sequence in context: A364315 A115368 A086932 * A221255 A341862 A256487

Adjacent sequences: A331759 A331760 A331761 * A331763 A331764 A331765

Keyword

nonn,tabl

Author

N. J. A. Sloane, Feb 04 2020

Status

approved