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 A292309 Numbers equal to the sum of three triangular numbers in arithmetic progression. 4
 9, 63, 84, 108, 234, 315, 459, 513, 570, 630, 759, 975, 1053, 1134, 1395, 1584, 1998, 2109, 2709, 2838, 2970, 3105, 3384, 3528, 3825, 4134, 4455, 4620, 4788, 4959, 5133, 5310, 5673, 5859, 6834, 7038, 7668, 7884, 8325, 8778, 9009, 9243, 9480, 10209, 10710, 11223 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Subsequence of A045943, because a(n) = 3*k*(k+1)/2 = 3*A000217(k) for some integer k. LINKS FORMULA a(n) = 3*A292310(n). EXAMPLE 9 = A000217(0) + A000217(2) + A000217(3) = 0 + 3 + 6, with 6 - 3 = 3 - 0 = 3. 513 = A000217(11) + A000217(18) + A000217(23) = 66 + 171 + 276, with 171 - 66 = 276 - 171 = 105. PROG (PARI) t=3; k=2; while(t<=5000, i=k; e=0; v=t+i; while(i>1&&e==0, if(issquare(8*v+1), m=3*t; e=1; print1(m, ", ")); i+=-1; v+=i); k+=1; t+=k) CROSSREFS Cf. A045943, A127329, A292310, A292313, A292314, A292316. Sequence in context: A341627 A159235 A181403 * A337236 A285456 A085645 Adjacent sequences:  A292306 A292307 A292308 * A292310 A292311 A292312 KEYWORD nonn AUTHOR Antonio Roldán, Sep 14 2017 STATUS approved

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Last modified June 21 10:09 EDT 2021. Contains 345360 sequences. (Running on oeis4.)