A194140 a(n) = Sum_{j=1..n} floor(j*(1+sqrt(3))); n-th partial sum of Beatty sequence for 1+sqrt(3).

2, 7, 15, 25, 38, 54, 73, 94, 118, 145, 175, 207, 242, 280, 320, 363, 409, 458, 509, 563, 620, 680, 742, 807, 875, 946, 1019, 1095, 1174, 1255, 1339, 1426, 1516, 1608, 1703, 1801, 1902, 2005, 2111, 2220, 2332, 2446, 2563, 2683, 2805, 2930, 3058

Offset

1,1

Links

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

Mathematica

c[n_] := Sum[Floor[j*(1+Sqrt[3])], {j, 1, n}];
c = Table[c[n], {n, 1, 90}]

Prog

(Python)
from sympy import integer_nthroot
def A194140(n): return n*(n+1)//2+sum(integer_nthroot(3*j**2, 2)[0] for j in range(1, n+1)) # Chai Wah Wu, Mar 17 2021

Crossrefs

Cf. A054088 (Beatty sequence for 1+sqrt(3)).

Sequence in context: A167543 A332495 A184976 * A029888 A194112 A005449

Adjacent sequences: A194137 A194138 A194139 * A194141 A194142 A194143

Keyword

nonn

Author

Clark Kimberling, Aug 17 2011

Extensions

Offset corrected by Alois P. Heinz, Mar 17 2021

Status

approved