A301853 Triangle read by rows: T(n,k) gives the number of distinct distances on an n X k pegboard, with n >= 1, 1 <= k <= n.

1, 2, 3, 3, 5, 6, 4, 7, 9, 10, 5, 9, 12, 14, 15, 6, 11, 15, 17, 19, 20, 7, 13, 18, 21, 24, 26, 27, 8, 15, 21, 25, 29, 31, 33, 34, 9, 17, 24, 29, 33, 36, 39, 41, 42, 10, 19, 27, 33, 38, 42, 45, 48, 50, 51, 11, 21, 30, 37, 43, 48, 51, 55, 58, 60, 61, 12, 23, 33, 41, 48, 53, 57, 61, 65, 68, 70, 71

Offset

1,2

Comments

Is k*(2*n - k + 1)/2 an upper bound on T(n, k)? - David A. Corneth, Mar 28 2018

Links

Peter Kagey, Table of n, a(n) for n = 1..10011 (first 141 rows, flattened)

Example

Triangle begins:
  1;
  2,  3;
  3,  5,  6;
  4,  7,  9, 10;
  5,  9, 12, 14, 15;
  6, 11, 15, 17, 19, 20;
  7, 13, 18, 21, 24, 26, 27;
  8, 15, 21, 25, 29, 31, 33, 34;
  9, 17, 24, 29, 33, 36, 39, 41, 42;
  ...

Prog

(PARI) T(n, k) = {my(d=[]); for (i=1, n, for (j=1, k, d = concat(d, (i-1)^2 + (j-1)^2); ); ); #vecsort(d, , 8); } \\ Michel Marcus, Mar 29 2018

Crossrefs

Cf. A047800, A225273, A301851.

Sequence in context: A003558 A216066 A234094 * A141419 A072451 A349669

Adjacent sequences: A301850 A301851 A301852 * A301854 A301855 A301856

Keyword

nonn,tabl

Author

Peter Kagey, Mar 27 2018

Status

approved