A371388 a(n) = 2*n*floor(n*(1 + sqrt(5))/2) - n^2. Main diagonal of A340429.

1, 8, 15, 32, 55, 72, 105, 128, 171, 220, 253, 312, 377, 420, 495, 544, 629, 720, 779, 880, 945, 1056, 1173, 1248, 1375, 1508, 1593, 1736, 1827, 1980, 2139, 2240, 2409, 2584, 2695, 2880, 2997, 3192, 3393, 3520, 3731, 3864, 4085, 4312, 4455, 4692, 4935, 5088, 5341

Offset: 1

Author

Paolo Xausa, Mar 21 2024

Keywords

• nonn
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A340429.

Cf. A000201, A001622.

Programs

Mathematica

Array[2 * # * Floor[# * GoldenRatio] - #^2 &, 100]

Python

from math import isqrt
def A371388(n): return n*((n+isqrt(5*n**2)&-2)-n) # Chai Wah Wu, Mar 21 2024

Formula

a(n) = 2*n*A000201(n) - n^2.