

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



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
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OFFSET

1,2


COMMENTS

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


LINKS

Table of n, a(n) for n=1..69.


PROG

(PARI) T(n, k) = {my(d=[]); for (i=1, n, for (j=1, k, d = concat(d, (i1)^2 + (j1)^2); ); ); #vecsort(d, , 8); } \\ Michel Marcus, Mar 29 2018


CROSSREFS

Cf. A047800, A225273, A301851.
Sequence in context: A003558 A216066 A234094 * A141419 A072451 A023156
Adjacent sequences: A301850 A301851 A301852 * A301854 A301855 A301856


KEYWORD

nonn,tabl


AUTHOR

Peter Kagey, Mar 27 2018


STATUS

approved



