A225253 Number of distinct values of the sum of 2 products of two 0..n integers.

1, 3, 8, 16, 27, 42, 59, 81, 105, 134, 167, 203, 241, 285, 331, 381, 436, 495, 556, 622, 690, 764, 841, 920, 1002, 1091, 1184, 1279, 1378, 1482, 1588, 1700, 1813, 1932, 2053, 2177, 2308, 2443, 2579, 2719, 2862, 3012, 3164, 3322, 3481, 3645, 3814, 3985, 4158, 4339

Offset: 0

Author

R. H. Hardin, May 04 2013

Keywords

• nonn

Examples

			a(3) = 16 as the possible products i*j where 0 <= i, j <= 3 are 0, 1, 2, 3, 4, 6, 9. From these numbers we can find the 16 distinct sums, listed with a few examples, 0, 1, 2, 3, 4, 5, 6, 7 = 3+4, 8, 9, 10, 11, 12 = 6+6, 13 = 4+9, 15, 18. - _David A. Corneth_, Sep 07 2023
		

Links

• David A. Corneth, Table of n, a(n) for n = 0..3000 (first 999 terms from R. H. Hardin)
• David A. Corneth, PARI program

Crossrefs

Row 2 of A225252.

Cf. A027384, A062854, A225254.

Programs

PARI

a(n) = #setbinop((x,y)->x+y, setbinop((x,y)->x*y, [0..n])); \\ Michel Marcus, Sep 06 2023

PARI

\\ See PARI link. David A. Corneth, Sep 07 2023

Python

from itertools import combinations_with_replacement
def A225253(n): return len({x+y for x,y in combinations_with_replacement({i*j for i in range(n+1) for j in range(i+1)},2)}) # Chai Wah Wu, Oct 13 2023

Extensions

a(0)=1 prepended by Alois P. Heinz, Oct 13 2023