A353386 Sums of two squares obtained by expanding a k X k matrix to (k+1) X (k+1) and taking the not yet seen squared distances of all positions in the matrix.

1, 2, 4, 5, 8, 9, 10, 13, 18, 16, 17, 20, 25, 32, 26, 29, 34, 41, 50, 36, 37, 40, 45, 52, 61, 72, 49, 53, 58, 65, 74, 85, 98, 64, 68, 73, 80, 89, 100, 113, 128, 81, 82, 90, 97, 106, 117, 130, 145, 162, 101, 104, 109, 116, 125, 136, 149, 164, 181, 200, 121, 122, 137, 146, 157, 170, 185, 202, 221, 242

Offset

1,2

Comments

The terms are a permutation of the positive terms of A001481.

Links

Table of n, a(n) for n=1..70.

Example

The sequence can be viewed as a table with line lengths A047800(k+1) - A047800(k), in which the not yet seen sums of squares form a table line. The table starts:
   1,  2,
   4,  5,  8,
   9, 10, 13, 18,
  16, 17, 20, 25, 32,
  26, 29, 34, 41, 50,
  36, 37, 40, 45, 52, 61, 72,
  49, 53, 58, 65, 74, 85, 98

Prog

(PARI) a353386(nmax)={my(v=vectorsmall(2*nmax^2)); for(n=1, nmax,
for(k=0, n, my(s=n^2+k^2); if(!v[s], print1(s, ", "); v[s]++)); print())};
a353386(11)

Crossrefs

Cf. A001481, A047800.

Cf. A353387 (first term in lines), A001105 (last term in lines).

Sequence in context: A125022 A362295 A069011 * A101185 A045702 A005658

Adjacent sequences: A353383 A353384 A353385 * A353387 A353388 A353389

Keyword

nonn,tabf

Author

Hugo Pfoertner, Apr 15 2022

Status

approved