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A071530
Numbers that are the sum of 3 triangular numbers in exactly 2 ways.
3
3, 6, 7, 9, 10, 13, 15, 17, 18, 19, 23, 24, 25, 26, 32, 33, 35, 38, 41, 44, 47, 54, 60, 62, 68, 69, 74, 80, 83, 89, 95, 99, 110, 113, 119, 128, 179, 194
OFFSET
1,1
COMMENTS
If it is required that the triangular numbers be positive, sequence A064825 results. - Jon E. Schoenfield, Jan 01 2020
EXAMPLE
From Jon E. Schoenfield, Jan 01 2020: (Start)
15 is a term of the sequence because there are exactly 2 ways to express 15 as the sum of 3 triangular numbers: 15 = 6 + 6 + 3 = 15 + 0 + 0.
60 is a term because there are exactly 2 ways to express 60 as the sum of 3 triangular numbers: 60 = 36 + 21 + 3 = 45 + 15 + 0.
12 can be expressed as the sum of 3 triangular numbers in 3 ways, so it is not a term: 12 = 10 + 1 + 1 = 6 + 6 + 0 = 6 + 3 + 3. (End)
PROG
(PARI) for(n=1, 150, if(sum(i=0, n, sum(j=0, i, sum(k=0, j, if(i*(i+1)/2+j*(j+1)/2+k*(k+1)/2-n, 0, 1))))==2, print1(n, ", ")))
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Jun 02 2002
EXTENSIONS
More terms from Vladeta Jovovic, Jun 07 2002
STATUS
approved