A194112 a(n) = Sum_{j=1..n} floor(j*sqrt(8)); n-th partial sum of Beatty sequence for sqrt(8).

2, 7, 15, 26, 40, 56, 75, 97, 122, 150, 181, 214, 250, 289, 331, 376, 424, 474, 527, 583, 642, 704, 769, 836, 906, 979, 1055, 1134, 1216, 1300, 1387, 1477, 1570, 1666, 1764, 1865, 1969, 2076, 2186, 2299, 2414, 2532, 2653, 2777, 2904, 3034, 3166

Offset

1,1

Links

Table of n, a(n) for n=1..47.

Mathematica

c[n_] := Sum[Floor[j*Sqrt[8]], {j, 1, n}];
c = Table[c[n], {n, 1, 90}]

Prog

(Python)
from sympy import integer_nthroot
def A194112(n): return sum(integer_nthroot(8*j**2, 2)[0] for j in range(1, n+1)) # Chai Wah Wu, Mar 17 2021

Crossrefs

Cf. A022842 (Beatty sequence for sqrt(8)).

Sequence in context: A184976 A194140 A029888 * A005449 A293401 A323038

Adjacent sequences: A194109 A194110 A194111 * A194113 A194114 A194115

Keyword

nonn

Author

Clark Kimberling, Aug 16 2011

Status

approved