A194137 - OEIS

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A194137

a(n) = Sum_{j=1..n} floor(j*sqrt(6)); n-th partial sum of Beatty sequence for sqrt(6).

2, 6, 13, 22, 34, 48, 65, 84, 106, 130, 156, 185, 216, 250, 286, 325, 366, 410, 456, 504, 555, 608, 664, 722, 783, 846, 912, 980, 1051, 1124, 1199, 1277, 1357, 1440, 1525, 1613, 1703, 1796, 1891, 1988, 2088, 2190, 2295, 2402, 2512, 2624, 2739, 2856

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..48.

MATHEMATICA

c[n_] := Sum[Floor[j*Sqrt[6]], {j, 1, n}];

c = Table[c[n], {n, 1, 90}]

PROG

(Python)

from sympy import integer_nthroot

def A194137(n): return sum(integer_nthroot(6*j**2, 2)[0] for j in range(1, n+1)) # Chai Wah Wu, Mar 17 2021