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 A354329 Triangular number nearest to the sum of the first n positive triangular numbers. 3
 0, 1, 3, 10, 21, 36, 55, 78, 120, 171, 210, 276, 351, 465, 561, 666, 820, 990, 1128, 1326, 1540, 1770, 2016, 2278, 2628, 2926, 3240, 3655, 4095, 4465, 4950, 5460, 5995, 6555, 7140, 7750, 8385, 9180, 9870, 10731, 11476, 12403, 13203, 14196, 15225, 16290, 17205 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..46. Wikipedia, Triangular number. FORMULA a(n) = (t^2+t)/2, where t = floor(sqrt(n*(n+1)*(n+2)/3)). EXAMPLE a(4) = 21 because the sum of the first 4 positive triangular numbers is 1 + 3 + 6 + 10 = 20, and the nearest triangular number is 21. MATHEMATICA nterms=100; Table[t=Floor[Sqrt[n(n+1)(n+2)/3]]; (t^2+t)/2, {n, 0, nterms-1}] PROG (PARI) a(n)=my(t=sqrtint(n*(n+1)*(n+2)/3)); (t^2+t)/2; vector(100, n, a(n-1)) (Python) from math import isqrt def A354329(n): return (m:=isqrt(n*(n*(n + 3) + 2)//3))*(m+1)>>1 # Chai Wah Wu, Jul 15 2022 CROSSREFS Cf. A000217, A000292, A053616, A229118, A354330. Sequence in context: A194141 A281153 A014105 * A146012 A027917 A038347 Adjacent sequences: A354326 A354327 A354328 * A354330 A354331 A354332 KEYWORD nonn,easy AUTHOR Paolo Xausa, Jun 04 2022 STATUS approved

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Last modified December 4 01:51 EST 2023. Contains 367541 sequences. (Running on oeis4.)