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A225253
Number of distinct values of the sum of 2 products of two 0..n integers.
2
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.
Sequence in context: A211480 A122796 A104249 * A254875 A025202 A131941
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 04 2013
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Oct 13 2023
STATUS
approved