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

0,2

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

Example

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

Prog

(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

Crossrefs

Row 2 of A225252.

Cf. A027384, A062854, A225254.

Sequence in context: A211480 A122796 A104249 * A254875 A025202 A131941

Adjacent sequences: A225250 A225251 A225252 * A225254 A225255 A225256

Keyword

nonn

Author

R. H. Hardin, May 04 2013

Extensions

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

Status

approved