A393283 A triangular array where each value is the sum of points on or adjacent to the ray connecting the value to the apex of the triangle, with first rows terms [0], [1,0].

0, 1, 0, 1, 1, 0, 2, 3, 2, 0, 4, 8, 7, 4, 0, 8, 20, 23, 18, 8, 0, 16, 48, 64, 55, 41, 16, 0, 32, 112, 178, 183, 155, 98, 32, 0, 64, 256, 461, 546, 448, 393, 221, 64, 0, 128, 576, 1182, 1496, 1515, 1334, 949, 506, 128, 0, 256, 1280, 2917, 4224, 4531, 3745, 3509, 2420, 1122, 256, 0

Offset

0,7

Comments

The construction takes a triangle with the first two rows {[0],[1,0]...}. Then for each subsequent row(n) n rays are drawn to the apex of the triangle. The ray tracks a sum for all nearby points, where the ray intersects a previous point, this value is included in the sum, where the ray passes between two points both values are included.

The leftmost diagonal will be 2^(n-2) for n>1.

The rightmost diagonal will always be 0.

Links

Table of n, a(n) for n=0..65.

Formula

T(n,k) = Sum_{i=0..n-1} Sum_{j=floor(i*k/n)..ceiling(i*k/n)} T(i,j) for n >= 2, with T(0,0) = 0, T(1,0) = 1, T(1,1) = 0.

A392906(n) = Sum_{k=0..n} (T(n,k) mod 2).

Example

Triangle beings:
  0;
  1, 0;
  1, 1, 0;
  2, 3, 2, 0;
  4, 8, 7, 4, 0;
  ...

Prog

(PARI) T(n)={my(v=vector(n+1)); v[1]=[0]; v[2]=[1, 0]; for(n=2, n, v[1+n] = vector(n+1, k, k--; sum(i=1, n-1, vecsum(v[1+i][i*k\n+1..(i*k-1)\n+2])))); v}
{ my(A=T(8)); for(i=1, #A, print(A[i])) } \\ Andrew Howroyd, Feb 08 2026

Crossrefs

Cf. A392906.

Sequence in context: A056888 A286297 A339451 * A111182 A178142 A375751

Adjacent sequences: A393280 A393281 A393282 * A393284 A393285 A393286

Keyword

nonn,easy,tabl

Author

Benjamin W P Cornish, Feb 08 2026

Status

approved