

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
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OFFSET

0,3


LINKS



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, nterms1}]


PROG

(PARI)
a(n)=my(t=sqrtint(n*(n+1)*(n+2)/3)); (t^2+t)/2;
vector(100, n, a(n1))
(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



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



