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

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

Crossrefs

Cf. A022840 (Beatty sequence for sqrt(6)).

Sequence in context: A267874 A194143 A194138 * A226292 A026052 A049616

Adjacent sequences: A194134 A194135 A194136 * A194138 A194139 A194140

Keyword

nonn

Author

Clark Kimberling, Aug 17 2011

Status

approved