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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 (list; graph; refs; listen; history; text; internal format)
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)/2-n, 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

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Last modified May 17 09:20 EDT 2022. Contains 353741 sequences. (Running on oeis4.)