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%I A354329 #44 Jul 15 2022 13:49:54
%S A354329 0,1,3,10,21,36,55,78,120,171,210,276,351,465,561,666,820,990,1128,
%T A354329 1326,1540,1770,2016,2278,2628,2926,3240,3655,4095,4465,4950,5460,
%U A354329 5995,6555,7140,7750,8385,9180,9870,10731,11476,12403,13203,14196,15225,16290,17205
%N A354329 Triangular number nearest to the sum of the first n positive triangular numbers.
%H A354329 Wikipedia, <a href="https://en.wikipedia.org/wiki/Triangular_number">Triangular number</a>.
%F A354329 a(n) = (t^2+t)/2, where t = floor(sqrt(n*(n+1)*(n+2)/3)).
%e A354329 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.
%t A354329 nterms=100;Table[t=Floor[Sqrt[n(n+1)(n+2)/3]];(t^2+t)/2,{n,0,nterms-1}]
%o A354329 (PARI)
%o A354329 a(n)=my(t=sqrtint(n*(n+1)*(n+2)/3));(t^2+t)/2;
%o A354329 vector(100,n,a(n-1))
%o A354329 (Python)
%o A354329 from math import isqrt
%o A354329 def A354329(n): return (m:=isqrt(n*(n*(n + 3) + 2)//3))*(m+1)>>1 # _Chai Wah Wu_, Jul 15 2022
%Y A354329 Cf. A000217, A000292, A053616, A229118, A354330.
%K A354329 nonn,easy
%O A354329 0,3
%A A354329 _Paolo Xausa_, Jun 04 2022

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