

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
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OFFSET

1,1


COMMENTS

If it is required that the triangular numbers be positive, sequence A064825 results.  Jon E. Schoenfield, Jan 01 2020


LINKS

Table of n, a(n) for n=1..38.


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)/2n, 0, 1))))==2, print1(n, ", ")))


CROSSREFS

Cf. A000217, A060773, A061262, A002636.
Cf. A064825, A002097, A008443, A064816.
Sequence in context: A138933 A288938 A282140 * A005767 A085837 A176237
Adjacent sequences: A071527 A071528 A071529 * A071531 A071532 A071533


KEYWORD

easy,nonn


AUTHOR

Benoit Cloitre, Jun 02 2002


EXTENSIONS

More terms from Vladeta Jovovic, Jun 07 2002


STATUS

approved



