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A071530 Numbers that are the sum of 3 triangular numbers in exactly 2 ways. 3

%I #15 Jan 08 2020 00:43:40

%S 3,6,7,9,10,13,15,17,18,19,23,24,25,26,32,33,35,38,41,44,47,54,60,62,

%T 68,69,74,80,83,89,95,99,110,113,119,128,179,194

%N Numbers that are the sum of 3 triangular numbers in exactly 2 ways.

%C If it is required that the triangular numbers be positive, sequence A064825 results. - _Jon E. Schoenfield_, Jan 01 2020

%e From _Jon E. Schoenfield_, Jan 01 2020: (Start)

%e 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.

%e 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.

%e 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)

%o (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,",")))

%Y Cf. A000217, A060773, A061262, A002636.

%Y Cf. A064825, A002097, A008443, A064816.

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, Jun 02 2002

%E More terms from _Vladeta Jovovic_, Jun 07 2002

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)